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data, forces, rudder, hydrodynamic, model, turning, mean, Figure, using, angle, propeller, motion, were, 23rd, Esso, ship, Osaka, estimated, test, with, results, coefficients, difference, force, sets, each, shown, from, that, different

Towing Tank

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Proceedings of the 23rd ITTC – Volume II 581

1.1. Membership and meetings

The Specialist Committee on Esso Osaka

was organized by five members and five

meetings were held.

The membership was

Prof. H. Kobayashi, Japan (Chairman)

Dr. J.J. Blok, Netherlands (Secretary)

Dr. R. Barr, USA

Dr. Y. S. Kim, Korea

Dr. J. Nowicki, Poland

Committee meetings were held five times

in the three years since last conference as

shown below,

1st July 2000 Boston, USA

2nd Nov. 2000 Wageningen, Netherlands

3rd May 2001 Ilawa, Poland

4th Oct. 2001 Tokyo, Japan

5th Feb. 2002 Taejon, Korea

1.2. Task proposed by 22nd ITTC

The studies on the Esso Osaka were carried out in Maneuvering Committee in 21st

ITTC. As a result of studies, following issues

are proposed to continue the analysis of the

Esso Osaka data in the following areas and to

organize a workshop to present the Esso

Osaka benchmark data and the results of the

analysis:

a) Reduce the scatter in existing data either

by eliminating suspect data sets, or by

stimulating new, benchmark quality experiments.

b) Compare propeller and rudder forces and

propeller-hull-rudder interactions.

c) Carry out a systematic series of simulations

using one reference mathematical model

(e.g. MMG with fixed propeller and rudder

forces and interactions) using available sets

of hull damping coefficients (linear and

nonlinear).

d) Compare the results of these systematic

simulations with available track data and

particularly the full scale trials data.

1.3. Use of Esso Osaka trial data as

benchmark

At the first meeting of the Maneuvering

Committee of the 21st ITTC in Trondheim,

Norway, the Committee selected an ITTC

benchmark ship for comparison of various

methods for predicting ship maneuverability.

Ships considered as this benchmark were the

Mariner, which was extensively investigated

by the Maneuvering Committee of the 11th

and 12th ITTC, the Esso Osaka for which unThe Specialist Committee on Esso Osaka

Final Report and Recommendations to the 23rd ITTC

582 The Specialist Committee on Esso Osaka

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usually complete trials results and model test

data were available, Crane (1979a) and Barr

(1993), and a more modern ship form, such as

one of the MARAD Series Models described

by Roseman (1987). The Esso Osaka was selected for the reasons noted in the following

sections.

The primary advantages of Esso Osaka trials data as a maneuvering benchmark were:

1. An unusually extensive set of trials of the

Esso Osaka at full load draft had been

conducted with unusual attention to

measurement accuracy, including correction of trials results for the effects of

ocean current measured during the trials,

Crane (1979a, 1979b).

2. Conduct of trials in deep water and in water depths equal to 1.5 and 1.2 times trials

draft.

3. Captive model tests or free running model

tests of the Esso Osaka had been carried

out by at least 20 different laboratories,

using models with lengths ranging from

1.65 to 8.125 meters.

4. Drawings of the Esso Osaka hull, propeller and rudder, required for the RANS

calculations planned by the Maneuvering

Committee, had been made available by

In addition, a significant body of Esso

Osaka captive model test data had been previously collected for a USA Marine Board study

of ship maneuvering simulators and simulation, Webster (1992), and an analysis of those

data for that study had been reported by Barr

The primary disadvantages of the Esso

Osaka as a maneuverability benchmark were:

1. The relative old hull form of a ship

launched in 1973.

2. The conduct of the benchmark trials before the availability of shipboard GPS and

the improved tracking accuracy available

with GPS.

3. The unavailability of good quality resistance or propulsion data, which would

also allow use of the Esso Osaka as a

benchmark for RANS flow calculations or

other ITTC studies.

Data for the Mariner were rejected as a

benchmark, despite the availability of extensive trials data and model test data because

maneuverability of that ship had already been

studied by ITTC Committees and because the

Mariner was an old and very atypical hull

form, and only four ships of the class were

ever built. No other comprehensive source of

ship and model test data for any ships of more

“modern” hull form could be identified by the

Committee.

The shortcomings of the Esso Osaka data

were considered minor when compared with

their advantages, and the Maneuvering Committee selected the Esso Osaka as its benchmark. The number of Ocean Engineering topics and Procedures should be continuously

maintained. A practical solution should be

found.

1.4. Lines on studies in Esso Osaka

Specialist Committee

In first stage of this study, proposed data

which were discussed in Maneuvering committee in 22nd ITTC were examined to know

the detail experimental conditions and analyzing procedures. It was confirmed that there are

mainly two kinds of mathematical models for

expression of ship maneuvering motion. The

proposed data may be different relating to the

mathematical model that is used for expression of motion. Two mathematical models are

selected to discuss the hydrodynamic coefficients and interaction forces. One of them is

MMG model (MMG, 1985), the other is whole

ship model: WSM. The details of the models

are explained in chapter 5 and chapter 6.

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Proceedings of the 23rd ITTC – Volume II 583

In chapter 3 in this report, the reasons of

scatter in proposed data sets are discussed.

There are many kinds of reason which occur

the scattering in measured hydrodynamic

forces and the coefficients. Therefore, in order

to discuss the benchmark data, the data of which

we can know the experimental conditions and

analyzing procedures should be chosen.

In chapter 2, the discussion on proposed

data in 21st ITTC and the scattering are analyzed. The potential reasons of scattering of

hydrodynamic coefficients shown in proposed

data are discussed in chapter 3. In chapter 4,

the proposed test data including full scale trial

tests and free running model tests are summarized. These results are target data of simulation using estimated hydrodynamic forces.

The discussion in chapter 5 and chapter 6 are

main parts of this report. The contents of proposed data are studied for estimation of maneuvering motion of Esso Osaka. The discussions on proposed data are studied based on

MMG model and Whole ship model. Finally,

Benchmark data on hull and propeller and

rudder interaction are proposed in conclusion.

2.1. Sources of hydrodynamic data

Force data for the Esso Osaka were available primarily in the form of hydrodynamic

coefficients derived from captive model test

data. Raw data or published plots of measured

forces versus test variables were available for

only a few tests, and the widely varying drift

angle and yaw rates of the tests made a meaningful comparisons of the force data problematic. 20 sets of hydrodynamic coefficients for

the Esso Osaka obtained by 18 laboratories

were collected and analyzed by the 22nd

ITTC Maneuvering Committee. The present

Committee has obtained four additional sets

of test data relating to WSM from laboratories

in Korea. The present Committee also decided

to eliminate from further consideration four of

the earlier data sets which were judged for

various reasons to be not reliable. As most

data were understood to have been obtained

using models with rudder installed, only those

data were considered. A total of 15 data sets

were therefore considered in order to investigate the scattering of predicted damping

forces and moments.

2.2. Summary of data comparisons

Predicted sway damping forces and yaw

damping moments were compared for data

sets understood to be for tests with rudder installed. In many cases the data source did not

indicate the operating condition of the propeller, or in some cases even if one was installed.

It was assumed that all data were obtained

with a propeller operating at either model or

ship self propulsion point.

Total damping forces and moments were

calculated for combination of five steady drift

angle, β = sin-1(v/U) and six non-dimensional

yaw rate, r' = rL/U. Figures 2.1 and 2.2 compare typical results for an eight degree drift

angle, for tests where a rudder was known or

believed to be installed. These figures show

rather large variations in total forces and moments, although the scatter is not as large as

that found by the 22nd ITTC Maneuvering

Committee due primarily to elimination of

suspect data sets having poor documentation,

apparent inconsistencies and/or highly atypical results. It was not possible to rationally

eliminate other data sets based on the information available.

2.3. Statistical Analysis of data scattering

In view of an inability to obtain data

needed to determining which data sets were

most reliable, it was decided to use a purely

584 The Specialist Committee on Esso Osaka

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statistical approach to select sets of data that

might be assumed most “reliable”. To do this,

the mean value and standard deviation of

sway force and yaw moment were determined

using all data sets of Figures 2.1 and 2.2, for

each of the 29 non-trivial combinations of

drift angle and yaw rate. These values were

used to determine, for sway force and yaw

moment for each of the N data sets and each

combination of drift angle and yaw rate, a difference of the value from the mean value for

all data sets. The “deviation” of a data set was

then defined to be the average, for all combinations of drift angle and yaw rate, of the difference of the values from the mean value,

divided by the standard deviation, or:

Dn={∑m[(Fn(βm,r'm)–Fmean(βm,r'm))/σ(βm, r'm)]}/M

where:

Dn is average deviation of sway force or yaw

moment, F, for test data set n;

Fn(βm,r'm) is force or moment for n-th data set

and m-th set of values of β and r';

Fmean(βm,r'm) is mean value of force for all

data sets for m-th set of values of β and r';

σ(βm,r'm) is standard deviation for all data sets

for m-th set of values of β and r';

M is the total combinations of β and r', considered, M = 29, m = 1, … 29

N is total number of data sets considered, n =

Values of the “deviation”, Dn, for each

data sets were independently calculated both

sway force and yaw moment. Data sets with

average “deviations” of about 1.0 or greater

were eliminated, and this process was repeated with the resulting reduced data set.

Again, data sets with an average “deviation”

of about one or more were eliminated, leaving

only five remaining data sets for both sway

force and yaw moment.

There is no certainty that this statistical

process has identified the most reliable data.

However, it is encouraging to note that the

same data sets were independently selected

for sway force and yaw moment, that the

variations of forces and moments among these

data sets are quite small.

Non-Dimens ional Y aw Rate - r '

Sw a y

or ce

Figure 2.1 Sway forces for +8° drift for selected data set.

Figure 2.2 Yaw moments for +8° drift for

selected data sets.

3.1. Potential sources of error with tests

PMM Tests

The varying rate of rotation during yawing tests

Inadequate numbers of motion cycles to

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Proceedings of the 23rd ITTC – Volume II 585

eliminate all effects of the starting transient and to permit accurate analysis of

the harmonic test data

Tests at reduced frequencies large

enough to introduce unsteady effects in

damping forces

Rotating arm test

Operation of model in its own wake after one revolution

Requirement to predict acceleration dependant forces which cannot be measured.

Systems identification (SI) of free-running

model tests or ship trials data

Systems Identification results are highly

sensitive to the quality of the data used and

the adequacy of the mathematical model. The

sensitivity of the process is illustrated by the

differences in the four sets of coefficients obtained using different models by Abkowitz

(1984). The validity of SI methods and results

has not in the past generally been established

by using the identified coefficients to predict

maneuvers different than those used for identification.

Model size

Model forces which are valid only for

the conditions (Reynolds number and

ambient turbulence level) of the particular test due to laminar flow (scale effects).

Wall effects when model length is large

compared with tank width or diameter,

particularly for large PMM motion amplitudes or large static drift angles.

It was concluded by the 22nd ITTC Maneuvering Committee that there was not conclusive evidence of significant scale effects in

the available Esso Osaka force data, although

large differences in forces were observed in

coefficients (forces) obtained at BMT using

the facilities and the same test procedures for

tests of 1.65 meter and 3.54 meter long models (Dand & Hood, 1983).

3.2. Potential sources of error of data

analysis methods

Methods used by various laboratories to

analyze captive model test data are rarely described in any detail. These methods can be

carried out using:

Purely mathematical methods, such as

regression analysis, using all test data or

a data set in which only clearly unreliable data points are eliminated.

An empirical approach in which the data

analyst assigns greater or lesser weight

to individual data points based on their

experience and knowledge of test conditions.

Data are analyzed or interpreted using a

particular mathematical model for hydrodynamic forces. Significantly different individual coefficients can thus be obtained when

using the same raw data. Ideally, these coefficients sets will predict similar forces and

moments, at least for drift angles, yaw rates,

rudder angles and propeller loadings which

are most typical of ship maneuvering, although this is by no means certain.

In following parts, the relation among the

experimental conditions and analyzing procedures and estimated hydrodynamic forces and

the coefficients are discussed.

3.3. Experimental conditions

The measured hydrodynamic forces are

changed due to following experimental conditions shown by Yoshimura (2001).

(1) The center of measuring forces

(2) The center of captive motion

(3) The freedom at captive model test

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(4) Error of towing speed

(5) Experimental condition w/wo propeller

(6) Propeller loading condition

The center of measuring forces

The measured hydrodynamic forces depend on the position of measuring instrument.

Longitudinal force and lateral force are not

affected by measuring position. However,

measured yaw moment is changed by the position of measuring instrument in the model

ship. Generally, motion equations are described based on the center of gravity. However, measuring forces are carried out based

on mid-ship position, because the center of

gravity of model ship is changed due to loading condition. Therefore, motion’s equation

are often described based on the center of

gravity, using hydrodynamic forces measured

at mid-ship position as following. The measured hydrodynamic forces depend on the position of measuring instrument. Longitudinal

force and lateral force are not affected by

measuring position. However, measured yaw

moment is changed by the position of measuring instrument in the model ship. Generally,

motion equations are described based on the

center of gravity. However, measuring forces

are carried out based on mid-ship position,

because the center of gravity of model ship is

changed due to loading condition. Therefore,

motion’s equation often described based on

the center of gravity using hydrodynamic

forces measured at mid-ship position as following,

XXrmvum GGG ==−&

YYrmuvm GGG ==−&

YxNNrI GGZZ −==&

where

X, Y, N: hydrodynamic forces measured at

mid-ship position

xG: distance from mid-ship to the center of

gravity

The relation between the captive position and

the measured hydrodynamic forces

The measuring hydrodynamic forces due

to turning motion are affected by the center of

turning motion where turning motion is activated. Measured forces are affected by experimental condition. Hydrodynamic coefficients are indicated in different values based

on the measuring point of Hydrodynamic

forces and center of enforced motion.

Table 3.1 shows the hydrodynamic coefficients based on different expression.

Table 3.1 Hydrodynamic coefficients acting

on bare hull Esso Osaka (Model ship length

2.5 m).

Motion CG CG Mid ship

Moment CG Mid ship Mid ship

X' vr–my 0.1871 0.1871 0.1905

X' vvvv 0.2786 0.2786 0.2743

Y'r–mx 0.0702 0.0556 0.0435

Y'vvv -1.2407 -1.2208 -1.2231

Y'vvr 0.2927 0.2644 0.1485

Y'vrr -0.3387 -0.3190 -0.3070

Y'rrr 0.0594 0.0536 0.0441

N' vvv -0.0597 0.0115 0.0120

N' vvr -0.2341 -0.2118 -0.2164

N' vrr 0.0994 -0.0795 0.0657

N'rrr -0.0149 -0.0103 -0.0081

The methods of installing model

To measure the hydrodynamic forces on

surge, sway and yaw, the motions on these

directions are fixed. The fixing condition of

other 3 motions such as pitch, roll and heave

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Proceedings of the 23rd ITTC – Volume II 587

affect the measuring hydrodynamic forces in

following cases.

In case of small GM at model test, the big

heeling angle induces the measuring hydrodynamic forces corresponding to that condition.

GM at model test must be same as full-scale

ship. In case of cramping the pitching and

heaving motion, the measuring hydrodynamic

forces are measured under the condition without sinkage. They differ from free running

condition in which sinkage is occurred depending on ship speed.

The experimental condition

When the hydrodynamic forces acting on

hull are estimated, the experimental condition

gives several effects on them. It is proper way

to carry out the captive model test using bare

hull. However, to reduce the experiment numbers, the captive test are carried out with propeller and rudder. And the hydrodynamic

forces acting on hull are estimated by subtracting propeller and rudder forces and their

interaction forces from measured total forces.

The estimated hydrodynamic forces acting on

hull by this way often show difference from

forces by measuring bare hull. As, the flow at

stern is affected by propeller and rudder, they

show difference ones. Especially, the suction

force caused by propeller affect the estimated

forces acting on hull.

The effect of propeller loading condition on

forces acting on hull

The hydrodynamic forces acting on hull

are affected by propeller’s loading condition.

Table 3.2 shows the relation between the hydrodynamic forces acting on hull and propeller loading conditions. The hydrodynamic

forces acting on hull measured in the condition of bare hull and in condition of propeller

and rudder equipped are shown. The propeller

loading are ship point and model point.

Table 3.2 Estimated Hydrodynamic coefficients Esso Osaka (Model ship length 2.5 m).

without

Propeller

Ship point Model point

X' vr–my 0.1905 0.1830 0.1946

X' vvvv 0.2743 0.1419 0.3172

Y'r–mx 0.0435 0.0572 0.0613

Y'vvv -1.2231 -1.3804 -1.2312

Y'vvr 0.1485 -0.0341 0.0128

Y'vrr -0.3070 -0.2713 -0.2882

Y'rrr 0.0441 0.0014 0.0092

N' vvv 0.0120 -0.0004 0.0049

N' vvr -0.2164 -0.2534 -0.2407

N' vrr 0.0657 0.0331 0.0341

N'rrr -0.0081 -0.0138 -0.0115

Error of towing speed

When CMT is carried out, the velocity of

each towing carriage is controlled based on

calculated velocity. As the motion characteristic of each towing carriage is different, actual

motion of each carriage cannot realize the calculated motion. Error of towing speed makes

the affect on the measuring hydrodynamic

force.

Figure 3.1 shows one example of the relation between the turn rate and combined speed

of tawing carriage.

Table 3.3 shows corrected hydrodynamic

forces based on the characteristics of towing

carriage motions and measured ones. The hydrodynamic coefficients concerning turn rate

(r) are changed.

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Rate of turn(deg/s)

Error of towing speed

(m/s)

Figure 3.1 The characteristics of towing carriage in CMT.

Table 3.3 Hydrodynamic coefficients measured by CMT (Model ship length 2.5 m).

Motion: Midship

Moment: Midship

Corrected

Hydrodynamic

Forces

Measured

Hydrodynamic

Forces

X'vv 0.0216 0.0378

X' vr–my 0.1905 0.1834

X’rr 0.0122 0.0178

X' vvvv 0.2743 0.1753

Y'r–mx 0.0435 0.0331

Y'vvv -1.2231 -1.2419

Y'vvr 0.1485 0.0162

Y'vrr -0.3070 -0.2521

Y'rrr 0.0441 0.0563

N' vvv 0.0120 0.0095

N' vvr -0.2164 -0.2217

N' vrr 0.0657 0.0555

N'rrr -0.0081 -0.0045

3.4. Conclusions

It has not been possible to explain the very

large differences in forces calculated using

hydrodynamic coefficients reported by the

22nd ITTC Maneuvering Committee. There

are many possible sources of differences, but

no primary sources have been clearly identified. 15 to 20 years after most tests Esso

Osaka tests were carried out, raw data are

largely unavailable and many of those responsible for tests and data analysis are no longer

active. It is therefore concluded that the reasons for the large observed data scatter must

remain largely undefined.

4.1. Full scale trial

The potential inaccuracies of any ship trials data are well recognized. These inaccuracies arise from the difficulty in correcting

measured results for effects of temporally and

spatially varying wind, current and waves and

inaccuracies in basic measurements such as

ship position. The special maneuvering Esso

Osaka trials of 1979 were planned and carried

out with unusual care, but available sensors

technology at that time was relatively unsophisticated, particularly the pre-GPS equipment used to record ship track. Finally, deep

water trials were carried out at a mean water

depth-to-draft ratio of 4.2, where bottom effects could exist, and water depth was not

constant in the shallow water trials despite the

great effort taken to select trials locations

where water depth was nearly constant.

Table 4.1 shows the main contents of sea

trial in deep water conditions. Figure 4.1

shows the turning trajectory with right rudder

angle 35 degrees and Figure 4.2 shows the

results of 10/10 zigzag maneuver.

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4.2. Free running model tests

The measured turning motion of free running models was used in evaluating the accuracy of simulations. Three sets of free running

model turning motion test results were available to be used. Two sets of tests were carried

out using models of 2.5 m in length and one

was carried out using a model of 4.6 m in

length.

Table 4.1 Main contents of Sea Trial (deep

water condition).

Type of

Trial

Rudder angle or

Rudder/heading angle

(deg)

Speed of

Approach

(knots)

Turning

maneuver

35, left rudder 7

Turning

maneuver

35, right rudder 7,10

Coasting

turning

maneuver

35, left rudder 5

Zigzag

maneuver

Coasting

Zigzag

maneuver

Zigzag

maneuver

Mean trajectories for these 3 models are

shown in Figure 4.3. A mean trajectory was

defined by calculating the mean X position at

every unit position on Y axis or by calculating

mean Y position at every unit position on X

axis. The results for the initial stage of turning

show significant differences, although steady

turning radii are nearly identical, ranging from

2.45L to 2.48L. The reasons for the difference

in initial turning shown in Figure 4.3 are not

clear. Therefore, the mean trajectory of the 3

tests was used as a baseline turning motion for

free running model tests.

Trials

a. The turning trajectory in Trial

r'(

rL

dr ift

in g an gl e( de g)

o t'=tUo/L

trials

b. The time history on ship’s speed, drifting angle

and rate of turn

Figure 4.1 The result of turning maneuver in

trial.

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ru dd er a ng le (d eg

he ad in g an gl e( de g) ra te o f t

ur n (r

o)

o dr ift

in g an gl e( de g) t'=tUO/L

trials

Figure 4.2 Zigzag maneuver in Trial (10/10

Zigzag).

mean

2.5m

4.6m

2.5m

Figure 4.3 The turning trajectory in free running model test (rudder angle +35°).

5.1. Mathematical model on MMG

Basic equation of motion

The mathematical model used in this study

is shown below.

YxNrI

Ymurvm

Xmvrum

Gzz &

where:

the origin of maneuvering motion is at the

center of gravity of the ship;

the origin of hydrodynamic force is at the

midship section on the centerline of the ship.

m: mass of a ship, Izz: moment of inertia of

yawing, X, Y and N are hydrodynamic forces

and moment acting on midship. xG represents

the location of C.G. in x-axis direction from

the midship.

These hydrodynamic forces and moments

can be divided into the following components.

where subscripts H, P and R refer to hull, propeller and rudder, respectively. Interaction

between hull and propeller and among hull,

propeller and rudder are contained in forces

and/or moment with subscript P and R.

Hydrodynamic forces and moment acting on

the hull

Hydrodynamic forces and yaw moments

acting on the hull are as follows:

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vvvv

rr yvr

vvxH

'v'X'r'X

'r'vm'X'v'XXumX'

rrr

vrr

vvr

vvvxrvyH

'r'Y'r'v'Y'r'v'Y

'v'Y'r'm'Y'v'Y'v'm'Y

rrr

vrr

vvr

vvvrvZZH

'r'N'r'v'N'r'v'N

'v'Nr'N'v'N'r'J'N

X(0) are measured from resistance test.

Hydrodynamic forces induced by propeller

The hydrodynamic forces induced by the

propeller are expressed as below:

321 JaJaaKT ++= (5.5)

nD u

)1( PP wuu −= (5.7)

where t: thrust deduction factor, n: propeller revolution, DP: propeller diameter, J: propeller advance ratio, a1, a2 and a3: constant for

propeller open characteristics

On wake fraction 1−wP, various estimation

formulas are proposed. Following two

mathematical models were used in this study.

[model 1]

10 )'()'()(11 rlkrlkJww PwPwPPP −+−+−=− ββ

(5.8a)

2100 )(1 PwPwwPP JaJaaJw ++=− (5.9)

[model 2]

0 )''('')1(1 rxvCrxvww PPPPP ++++−=− τ (5.8b)

Hydrodynamic force and yaw moment induced by rudder

The hydrodynamic forces induced by rudder are described below, in terms of rudder

normal force FN, rudder angle δ, and rudder to

hull interaction coefficients tR, aH, xH:

δsin)1( NRR FtX −−= (5.10a)

δcos)1( NHR FaY +−= (5.10b)

δcos)( NHHRR FxaxN +−= (5.10c)

5.2. Hydrodynamic forces acting on hull

As stated previously, hydrodynamic coefficients can have different values as a result of

differences of experimental condition, analysis procedures and mathematical models used.

The effect of these issues on the data being

considered here cannot be quantified. Therefore, it is not meaningful to compare the different sets of data directly.

Data from four sets of tests for which detailed information were available for consideration. The hydrodynamic coefficients obtained from these four sets of tests using different procedures, were unified to a single set

of test conditions and the unified data were

used to simulate maneuvering of the Esso

Osaka.

The experimental conditions for the four

selected tests are shown in Table 5.1. Bare

hull hydrodynamic coefficients derived from

the test results, unified to the same test conditions, are shown in Table 5.2. Longitudinal

hydrodynamic forces for the 4 model ships are

shown in Figure 5.1. Lateral force and yawing

moment are shown in Figure 5.2 and Figure

5.3. In Table 5.2 and in all figures showing

hydrodynamic forces, mean hydrodynamic

coefficients, and resulting mean hydrodynamic forces, calculated using each of the 4

models, are also shown.

Longitudinal forces, X', for the 4 model

shown in Figure 5.1 show similar tendency for

small drift angles and turning rates. With

large yaw rate and drift angle or sway rate, the

hydrodynamic forces show significant differences. Lateral force, Y', shows a similar tendency but with smaller difference than those

for X'. Yaw moment, N', also shows similar

tendency, with the differences between the 4

sets of hydrodynamic forces increase as the

combined yaw and sway rates increase.

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Table 5.1 Experimental conditions.

Research Institute A B C D

Length of model ship 6.0 m 4.6 m 4.0 m 2.5 m

Kind of test C.M.T. C.M.T. C.M.T. C.M.T.

Model ship speed

Froude Number

0.699 m/s, Fn=0.0912 0.611 m/s, Fn=0.0910 0.400 m/s, Fn=0.0639 0.450 m/s, Fn=0.0911

Revolution of propeller ship point model point bare hull model point

appendages Propeller, rudder Propeller, rudder none Propeller, rudder

Measured items

Hull forces, propeller thrust,

rudder normal forces

Hull forces, propeller

thrust, rudder normal

forces

Hull forces

Hull forces, propeller thrust,

rudder normal forces

Captive point C.G. C.G. C.G. C.G.

The measurement center of

the yaw moment

Mid Ship C.G. C.G. Mid Ship

Freedom of ship motion

Fore: pitching Free

Aft.: pitching & surging Free

Free to pitching, rolling

Free to pitching, heave,

rolling Free to pitching, rolling

Experimental range

Coupling motion range at CMT

Coupling motion range at

Coupling motion range at

Coupling motion range at

While the different methods of captive

model test and different analyzing procedures

were done, we can compare the unified values

by coherent converting way concerning the

contents. As a result, it is clarified that the

scattering among them are small. In next section, the effects of the varieties in data on the

estimation of motion are discussed.

6.0m 4.6m

4.0m 2.5m

mean data

r'

Figure 5.1 Longitudinal force (X'H).

6.0m 4.6m

4.0m 2.5m

mean data

r'

Figure 5.2 Lateral force (Y'H).

6.0m 4.6m

4.0m 2.5m

mean data

r'

Figure 5.3 Yaw moment (N'H).

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Table 5.2 Hydrodynamic coefficients.

6.0 m 4.6 m 4.0 m 2.5 m Mean data

Motion C.G. C.G. C.G. C.G. C.G.

Moment Mid Ship Mid Ship Mid Ship Mid Ship Mid Ship

Propeller revolution Ship point Model point ― Model point ―

appendages

Propeller &

rudder

Propeller &

rudder

― Propeller &

rudder

Non-dimensional forms: 22

22dUL

5.3. Estimation on ship’s motion

Estimation using original proposed data

For studying the effect of different hydrodynamic forces acting on hull, the forces

caused by propeller and rudder were estimated

using the following mathematical model, designated PR model-1, and the associated coefficients given in Table 5.3.

Table 5.3 The coefficient in (PR model-1).

1–wP0 τ C'P x'P k ε

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(PR model-1)

2)()(11 'rx'vC'rx'vww 'P

u u

)( 'r'l'vv RR += γ (5.12)

)(tan)( 10 RRR uv

RRRN UfAF αρ α sin2

RRR vuU +=

(1) Predicted turning motion

The turning motions estimated using the 4

sets of originally proposed coefficients are

shown in Figure 5.4. Turning trajectories are

shown in Figure 5.4.a and ship’s velocity,

drift angle and non-dimensional rate of turn

are shown in Figure 5.4.b. Mean results from

free-running model tests are also shown in

Figures 5.4.a and 5.4.b. All simulated turning

trajectories are similar, and the simulated initial turning motions are smaller than the

measured initial turning motion. Simulated

advances with the different data sets have differences of –0.5% to 2.7% from that simulated using the mean hydrodynamic coefficients, while estimated steady turning diameters have differences of –0.6% to 3.3% from

those for the mean hydrodynamic coefficients.

(2) Zigzag test

In Figure 5.5, results for a simulated 15-15

zigzag maneuver results and results for this

maneuver obtained from free running tests of

a 6.0 m model are presented. The results include rudder angle, turning angle, ship’s speed

and drift angle. Up to the second overshoot,

all simulated results are similar and all are in

good agreement with the free running test results.

The difference among the results estimated by using data from each institute shows

very small. Concerning the varieties on the

results of free running model test, it is difficult to judge whether the data proposed by

different institute is good or bad.

Free run(mean)

Original data 6.0m

Original data 2.5m

Original data4.6m

Original data 4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr ift

in g an gl e (d eg

o t'=tUo/L

Free run(2.5m)

Original data 6.0m Original data 4.6m

Original data 4.0m Original data 2.5m

mean data

b. The time history on ship’s speed, drifting

angle and rate of turn ( rudder angle +35°)

Figure 5.4 The estimation of turning motion

estimated by using the hydrodynamic coefficients of each institute.

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The effect of variety of estimated hydrodynamic forces on motion estimation

It is clarified in previous studies that the

effect of difference of estimated hydrodynamic forces shows small. In this section, the

effect on simulated motions of changes in an

individual hydrodynamic force component, X,

Y or N, is discussed.

ru dd er a ng le (d eg

ra te o f t

ur n( de g/ se c) sh ip 's v el oc ity

(m /s

dr ift

in g an gl e( de g) Time(sec)

he ad in g an gl e( de g) Free run(6.0m) 6.0m 4.6m

4.0m 2.5m mean data

Figure 5.5 The Zigzag maneuver estimated

by using the hydrodynamic coefficients of

each institute (15/15 Zigzag).

(1) Effect of individual forces on turning

motion

(A) The effect of difference in longitudinal

force

The effect on simulated results of the difference in the surge force, X, proposed by

each institute was studied by conducting

simulations in which Y and N were defined to

have the mean values for all data. The resulting trajectories are shown in Figure 5.6.a and

time histories of ship’s speed, drift angle and

turn rate are shown in Figure 5.6.b.

Free run(maen)

6.0m

2.5m

4.6m

4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr ift

in g an gl e (d eg

o t'=tUo/L

Free run(2.5m)

6.0m 4.6m

4.0m 2.5m

mean data

b. The time history on ship’s speed, drifting

angle and rate of turn ( rudder angle +35°)

Figure 5.6 The turning motion estimated by

using X'H each institute (Y'H, N'H: mean data

of each institute are used).

596 The Specialist Committee on Esso Osaka

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The differences in X, as shown in Figure

5.1, make no significant difference in turning

motion. The maximum difference of turning

diameter simulated using the four different X

forces and the mean hydrodynamic coefficients, the maximum difference of estimated

diameter of turning circle is 3.2%, it is very

small. For every set of X force data the simulated rate of turn in steady turning motion is

smaller than that measured in the free running

model tests.

(B) The effect of difference in lateral force

The effect on simulated results of the difference in the surge force, Y, proposed by each

institute was studied by conducting simulations

in which X and N were defined to have the

mean values for all data. The resulting trajectories are shown in Figure 5.7.a, and time histories of ship’s speed, drift angle and turn rate are

shown in Figure 5.7.b. The differences in Y, as

shown in Figure 5.2, make no significant difference in drift angle or in turning motion. The

difference of Yv among the institutes are 13.0%

to -0.5% comparing to mean value and the difference of Yr–mx are 15.0% to -35.0%. The

maximum difference of the advances and turning diameters simulated using the four different

Y forces and the mean values of Y are -0.5% to

-0.8% and -0.2% to 0.8%, respectively. For

every set of Y force data the simulated rate of

turn in steady turning motion is smaller than

that measured in the free running model tests.

(C) The effect of difference of estimated

turning moment

The effect on simulated results of the difference in the yawing moment, N, proposed

by each institute was studied by conducting

simulations in which X and Y were defined to

have the mean values for all data. The resulting trajectories are shown in Figure 5.8.a and

time histories of ship’s speed, drift angle and

turn rate are shown in Figure 5.8.b. Although

the differences in N, as shown in Figure 5.3

make no significant difference in turning motion, the turning trajectories show larger differences than do those obtained with different

values of X and Y.

4 Free run(mean)

6.0m

2.5m

4.6m

4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr ift

in g an gl e( de g)

o t'=tUo/L

Free run(2.5m)

6.0m 4.6m

4.0m 2.5m

mean data

b. The time history on ship’s speed, drifting

angle and rate of turn ( rudder angle +35°)

Figure 5.7 The turning motion estimated by

using Y'H each institute (X'H, N'H: mean data

of each institute).

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The difference of Nv among the institutes

are 9.5% to 1.0% comparing to mean value

and the difference of Nr are 7.0% to -10.%.

The maximum difference of the advances and

turning diameters simulated using the four

different Ns and the mean values are -0.6% to

3.0% and -2.3% to 2.8%, respectively.

(2) Effect of individual force on zigzag

motion

(A) The effect of difference of estimated

longitudinal force

In this section, the effects of difference of

longitudinal force X on the zigzag motion estimation are discussed. For this study, the effects

of using the X proposed by each institute are discussed, using the mean values of Y and N. Time

histories of rudder angle, turning angle, ship’s

speed and drifting angle are shown in Figure 5.9.

The use of the different values of X of Figure 5.1

has no significant effect on zigzag motions, and

all results show good agreement with free running model test results up to 2nd overshoot.

Comparing to the estimated 1st and 2nd overshoot angles of 5.4 degree and 10.1 degree obtained using mean values of all hydrodynamic

coefficients, the different values of X gave values of 5.1 to 5.8 degrees for the 1st overshoot

angle and 10.7 to 10.8 degree for the 2nd overshoot angle. These differences are small.

(B) The effect of difference of estimated

lateral force

In this section, the effects of difference of lateral force Y on the zigzag motion estimation are

discussed. For this study, the effects of Y proposed by each institute are discussed. X and N

defined by mean of them are applied. The time

histories of rudder angle, turning angle, ship’s

speed and drifting angle are shown in Figure 5.10.

The difference of estimated Y makes big effects

on the estimation of overshoot angle and drifting

angle. Comparing to the estimated 1st and 2nd

overshoot angle by using mean hydrodynamic

coefficients that are 5.4 degree and 10.1 degree,

the range of estimated 1st overshoot angle is 5.1

to 6.5 degree and the range of estimated 2nd overshoot angle is 9.4 to 12.5 degree.

Free run(mean)

6.0m

2.5m

4.6m

4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr fit

in g an gl e( de g)

o t'=tUo/L

Free run(2.5m)

6.0m 4.6m

4.0m 2.5m

mean data

b. The time history on ship’s speed, drifting angle

and rate of turn ( rudder angle +35°)

Figure 5.8 The turning motion estimated by

using N'H each institute (X'H, Y'H: mean data

of each institute).

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ru dd er a ng le (d eg

ra te o f t

ur n( de g/ se c) sh ip 's v el oc ity

(m /s

dr ift

in g an gl e( de g) Time(sec)

he ad in g an gl e( de g) Free run(6.0m) 6.0m 4.6m

4.0m 2.5m mean data

Figure 5.9 The Zigzag maneuver estimated

by using X'H each institute (15/15 Zigzag)

(Y'H, N'H: mean data of each institute).

(C) The effect of difference of estimated

turning moment

In this section, the effects of difference of

turning moment N on the motion estimation are

discussed. For this study, the effects of N proposed by each institute are discussed. X and Y

defined by mean of them are applied. The time

histories of rudder angle, turning angle, ship’s

speed and drifting angle are shown in Figure

5.11. The difference of estimated N shown in

Figure 5.3 dose not make big difference on

zigzag motion and they show similar estimation up to 2nd overshoot. And they show good

agreement to free running model test up to 2nd

overshoot angle. Comparing to the estimated

1st and 2nd overshoot angle by using mean hydrodynamic coefficients that are 5.4 degree and

10.1 degree, the range of estimated 1st overshoot angle is 5.0 to 5.7 degree and the range

of estimated 2nd overshoot angle is 9.3 to 10.5

degree. It is small.

ru dd er a ng le (d eg

ra te o f t

ur n( de g/ se c) sh ip 's v el oc ity

(m /s

dr ift

in g an gl e( de g) Time(sec)

he ad in g an gl e( de g) Free run(6.0m) 6.0m 4.6m

4.0m 2.5m mean data

Figure 5.10 The Zigzag maneuver estimated

by using Y'H each institute (15/15 Zigzag)

(X'H, N'H: mean data of each institute).

As the stability index is defined by certain

Y and N coefficients, the change of Y make the

change of stability index rather than the change

of N. Values of Yv for the four sets of data

differ by 13.0% to -0.5% from the mean

value of Yv and values of Yr–mx differ by

15.0% to -35.0% from the mean value. Values of Nv and Nr differ from the mean values by

9.5% to 1.0% and 7.0% to -10.0%, respectively.

The stability index obtained using the

original hydrodynamic coefficients proposed

by the four institutes differ by 32.0% to -23.0%

from those obtained using the mean coeffi 23rd International

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Proceedings of the 23rd ITTC – Volume II 599

cients. The range of stability obtained using

only individual values of Y differ widely from

the mean, by 52.0% to -24.0%. The range of

stability indexes due to use of different values

only of N is 0% to -26.0%. Therefore, Y forces

have a significantly larger effect on stability

index than does yaw moments, N. By this reason, the estimated zigzag motions based on the

change of Y show bigger scattering rather than

ones based on the change of N. Figure 5.12

shows the relation between stability index of

bare hull and 1st overshoot angle. The range of

stability index due to use of different Y shows

wider range than that due to change of N. The

accuracy of the Y forces thus has a big effect on

the stability index and the accuracy of simulated zigzag motion.

ru dd er a ng le (d eg

ra te o f t

ur n( de g/ se c) sh ip 's v el oc ity

m /s

dr ift

in g an gl e( de g) Time(sec)

he ad in g an gl e( de g) Free run(6.0m) 6.0m 4.6m

4.0m 2.5m mean data

Figure 5.11 The Zigzag maneuver estimated

by using N'H each institute (15/15 Zigzag)

(X'H, Y'H: mean data of each institute).

1s t O

ve rs ho ot a ng le (d eg

Stability index (bare hull condition)

The hydrodynamic derivatives

1s t O

ve rs ho ot a ng le (d eg

The derivatives of Y'H prposed by the institute

1s t O

ve rs ho ot a ng le (d eg

(mean data)

(mean data)

(mean data)

Stability index (bare hull condition)

Stability index (bare hull condition)

proposed by each institute

X'H,N'H mean derivatives

The derivatives of N'H prposed by the institute

X'H,Y'H mean derivatives

Figure 5.12 The relation between the 1st

overshoot angle and stability index.

5.4. Hydrodynamic forces due to

propeller, rudder and

hull/propeller/rudder interactions

Formulas on Hydrodynamic forces caused by

propeller and rudder

Several mathematical models for propeller,

rudder and interaction forces have been proposed by different institutes. In this section, the

effect on simulated motions of the mathematical model used to predict propeller, rudder and

interaction forces is discussed. For this purpose, model PR model-1, which was discussed

earlier, and a second model, PR model-2,

which is described below, have been used.

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(PR model-2)

210 )()()(11 'rlk'rlkJww

Pw

2100 )(1 PwPwwPP JaJaaJw ++=− (5.17)

kw u u

210 )()(11 'rlk'rlkww

Pw

u

RRRN sinUfAF αρ α

RRR vuU += (5.24)

The turning motion simulated using PR

model-1 and PR model-2 are shown in Figure

5.13.a. Maximum advance and steady turning

diameter estimated using PR model-1 are

3.12L and 2.38L, respectively. Those estimated using PR model-2 are 3.01L and 2.71L.

Those measured in free running model test are

2.94L and 2.46L. Figure 5.13.b shows rudder

normal force, longitudinal inflow velocity at

rudder position and effective inflow angle calculated using both models. The initial stage of

turning is estimated different. The differences

in the simulated results are due to both the

details of the mathematical model and the empirical constants used with each model.

Flow straightening constant

One of specific characteristics of MMG

model is to express the hydrodynamic forces

caused by propeller and rudder and interaction

among hull, propeller and rudder correctly

based on the hydrodynamic phenomenon.

There are several constant in the PR model-1

mentioned above. The flow straightening constant γ has an important effect on rudder force.

Free run(mean)

6.0m

2.5m

4.6m

4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr fit

in g an gl e( de g)

o t'=tUo/L

Free run(2.5m)

6.0m 4.6m

4.0m 2.5m

mean data

b. The time history on rudder normal force,

inflow velocity at rudder and effective rudder

angle (rudder angle +35°).

Figure 5.13 The turning motion estimated by

PR-model-1 and PR-model-2.

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Free run(mean) Original (γ =0.4080)

Free run(mean) original (γ =0.4080)

a. The turning trajectory (γ increase) b. The turning trajectory (γ decrease)

(k g) u R

(m /s

(d eg

Original γ =0.4080

Time (sec)

(k g) u R

(m /s

(d eg

Original γ =0.4080

time(sec)

c. The time history on rudder normal force,

inflow velocity at rudder and effective rudder

angle (γ increase)

d. The time history on rudder normal force,

inflow velocity at rudder and effective rudder

angle (γ decrease)

Figure 5.14 The estimation accuracy of γ on turning motion.

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Figure 5.14 shows the relation between the

turning motion and flow straightening constant. Simulated turning trajectories for incremental increases of 10.0% in the value of γ

are shown in Figure 5.14.a and those for

10.0% decreases in the value of γ are shown

in Figure 5.14.b. In Figures 5.14.c and 5.14.d,

the time histories on rudder normal force,

longitudinal flow velocity at the rudder position and effective inflow angle to the rudder

are shown. A change in γ results in a change

in inflow angle and rudder normal force. The

value of γ determines the motion at both the

initial stage and steady stage of turning. The

effect on turning of the investigated changes

of γ is much larger than the effect of the differences in hydrodynamic coefficients.

Constant used with PR model-2

In this section, the effects of element in

(PR model-2) are discussed by following

methods.

(1) (1–wP0): wake fraction at propeller and

propeller loading condition

(PR model-2) express that propeller loading condition affects the change of wake fraction at propeller position. We discussed this

effect provided that other effects are taken

into account. It means that the changes of

wake fraction at propeller and rudder position

are taken into account.

(2) (1–wP): wake fraction at propeller and

drifting and yawing condition

(PR model-2) express that drifting and

yawing condition affects the change of wake

fraction at propeller position. We discussed

this effect provided that the following conditions are taken into account. It means that the

changes of wake fraction at rudder position

are taken into account and wake fraction at

propeller position is not affected by propeller

loading condition.

Free run(mean)

6.0m

2.5m

4.6m

4.0m

mean data

a. The turning trajectory (rudder angle +35°)

r'(

rL

dr fit

in g an gl e( de g)

o t'=tUo/L

Free run(2.5m)

6.0m 4.6m

4.0m 2.5m

mean data

b. The time history on propeller thrust, inflow

velocity at rudder and rudder normal force

(rudder angle +35°).

Figure 5.15 The influence of mathematical

model of 1–wP on the turning motion.

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Figure 5.15 shows the results of comparison mentioned above. The estimated result

containing all of factors in (PR model-2) is

also indicated in Figure 5.15. Propeller loading condition in wake fraction at propeller affect small change in motion estimation. On

the other hand, when wake fraction at propeller position is assumed as constant during

maneuvering motion, propeller advance ratio

J is constant. Then the rudder effect is

overestimated caused by overestimating

longitudinal inflow velocity at rudder

position: uR. Figure 5.15.b shows these situations.

The change of wake fraction due to maneuvering motion has an important effect on

propeller and rudder forces and on simulated

maneuvering motions.

5.5. Conclusions

The results of available captive model

tests reflect differences in experiment condition, mathematical model used, etc. However

we can compare hydrodynamic forces proposed by different institutes by unifying them

by correcting for differences in test conditions. After such unification, simulated results

with the different data show small differences

in simulated maneuvering motion. The scattering of results is small because the various

institutes understood the concept of the MMG

model and thus carried out coherent experiment and analysis of data.

For the future direction, we would like to

point out that it is important to carry out experiments and data analysis using a unified

approach, and essential to clearly define test

conditions and analysis procedures when attempting to compare results from different

institutes.

As a part of benchmark study, comparative

simulations of Esso Osaka tanker have been

done with selected datasets of ‘whole ship

model’ type mathematical model. There are

many available datasets of whole ship model

type mathematical model which have been

submitted to ITTC committee. But it is found

that most of them are not suitable for simulation study in this time because of insufficient

information on their data and mathematical

model. For full simulation, some need further

data and some mathematical are not clear.

There are also some datasets which are believed to have typographic errors. Therefore,

it is not easy to reproduce same simulation

results with their original results using only

submitted information. For this reason, only

three datasets from KRISO (Korea Research

Institute of Ships & Ocean Engineering),

HSMB (Hydronautics Ship Model Basin) and

SNU (Seoul National University) are selected

as reference datasets.

This section presents the comparison between simulation results by three different

models and full-scale trial data. Hydrodynamic

forces predicted by three models are also compared each other at the range of motion variables experiencing during standard maneuvers.

6.1. Mathematical models and PMM test

results

Mathematical models of ship maneuvering

motion, PMM test conditions and hydrodynamic coefficients from three organization are

summarized here. All definition of notations

and nondimensionalization follows ITTC convention.

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The mathematical model of KRISO are as

follows (Kim, 1988 ).

(Thrust))Resistance(

rXX

rXX

vXX

vrXuXrxvrum

rrrr

vvvv

vruG

vrYvrY

rrYY

vvYY

rYY

vYY

rYvYYYrxurvm

vrvrr

rrrr

vvvv

rr vv rvooG &&&& &&

|| || vYY vv δδδ δδδ ++ (6.2)

vNN

vrNvrN

rNN

vvNN

rNN

vNNrN

vNNNurvmxrI

vv vrvrr

rrrr

vvvv

rr vvr

vooGz

where (Resistance) and (Thrust) are measured

from the resistance test and propeller open

water and self propulsion test.

KRISO has conducted HPMM tests using a

model ship with a length of 6.5 m in the towing

tank whose dimensions are 200 m × 16 m × 7 m.

All the tests were carried out with fully appended model and with the propeller operating

at the ship propulsion point.

Test programs are summarized in Table

6.1 and Table 6.2. Hydrodynamic coefficients

of KRISO are summarized in Table 6.3. Here,

all the force coefficients are taken with the

origin at the ship center of gravity.

Table 6.1 Static Test Program of KRISO.

Type

Drift

Angle

(deg)

Rudder

Angle

(deg)

Model

Speed

(m/s)

Speed

Rudder

Static

Drift

Drift

Rudder

Table 6.2 Dynamic Test Program of

Type

Drift

Angle

(deg)

Rudder

Angle

(deg)

Model

Speed

(m/s)

Speed

Rudder

Static

Drift

Drift

Rudder

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Table 6.3 Hydrodynamic coefficients of KRISO.

Coefficient Value×105 Coefficient Value×105 Coefficient Value×105

'X vv 0. 'Yv -1930.9 'Nv -761.2

'Y |v|v -4368.1 'N |v|v 118.2

'X rr 133.1 'Yr 561.4 'Nr -322.0

'X vr 1530.1 'Y |r|r 206.5 'N |r|r -113.6

'Yvrr -3428.2 'Nvrr 338.2

'Y |v|r 321.8 'N |v|r -361.7

'Y vvδ -2281.3 'N vvδ -109.9

'Yo 2.0 'No -1.0

'X vvη 0. 'Yvη -349.2 'Nvη -28.7

'Y |v|v η 0. 'N |v|v η 24.1

'X rrη 0. 'Yrη 54.7 'Nrη -9.6

'Y |r|r η 0. 'N |r|r η 0.

'Yoη 2.0 'Noη -1.0

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The mathematical model of Hydronautics

are as follows (Hydronautics, 1980).

)|sin|'|cos|'('

RUDp

iii

vvvv

rr uvru

XuL

cbauL

vXXL

rXL

vrXXuX

Lrxvrum

YwL

YuLUvrYL

vvYuvY

vvYuvY

rvY

urYurYvY

rrYrYLrxurvm

p RUDpvrr

vvv

vvv

rv rrv

rrrG

)'v|v|(ηN

)'uv(ηN'v|v|N'uvN

/U'vrNL

'|v|rN)'ur(ηN'urNLρ

rL u

'r|r|Nr'N

v'NL

ur)v(mxrI

*pRUDp

v|v|η

vηv|v|v

Rvrr

|v|rrηr

r|r|r

vGz

tanh1212

Hydronautics conducted HPMM tests using a

model ship with a length of about 24 ft in the towing

tank whose dimension is 128 m × 7.6 m × 3.9 m.

All the tests were carried out with fully appended

model and with the propeller operating at the ship

propulsion point.

Hydronautics have carried out HPMM

tests at three depths. But, only the data at deep

water will be shown here. Test programs and

hydrodynamic coefficients are summarized in

Tables 6.4, 6.5 and in Table 6.6 respectively.

Here, all the force coefficients are defined at

the ship center of gravity.

Table 6.4 Static Test Program of Hydronautics.

Type

of Test

Drift

Angle

(deg)

Rudder

Angle

(deg)

Model

Speed

(m/s)

Propulsion 0 0

Static

Drift

Static

Rudder

Rudder

and

Drift

Table 6.5 Dynamic Test Program of Hydronautics.

Type

of Test

Drift

Angle

(deg)

Rudder

Angle

(deg)

Model

Speed

(m/s)

Propulsion 0 0

Static

Drift

Static

Rudder

Rudder

and

Drift

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Table 6.6 Hydrodynamic Coefficients of Hydronautics.

Coefficient Value Coefficient Value Coefficient Value

'X vv 0.0035 'Nr -0.00353 1c 0.001244

rr'X 0.0003 |'r|rN -0.00069 2a -0.00085

'X vvη 0.0021 'N |v|v 0.0 2c 0.000712

'Yr 0.00595 2vr

'Yrη 0.00060 |v|r'N -0.0034 d 0.33

'Yvvη 0.0 f 0.077

'Yvrr -0.0156 |v|r'Y 0.0075 wa 0.0

'Y∗ 0.0 wb 0.42

Table 6.7 Hydrodynamic Coefficients by SNU.

Coefficient Value Coefficient Value Coefficient Value

'Yvvv 0.095876 'N vvv -0.004756

'X rr -0.002770 'm'Yr − -0.011914 'Nr -0.003774

'Yrrr -0.010450 'Nrrr -0.000594

'm'X vr + 0.028172 'Yvvr 0.024019 'Nvvr -0.021079

'X vvrr 0.033843 'Yvrr -0.010450 'Nvrr 0.002357

'Yeee 0.000519 'Neee -0.000026

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The mathematical model of SNU are as

follows (Rhee, Key. P., et al., 1993).

[ ] )()( ResistanceThruste'XcL

U/rv'Xr'XL

v'XL

vrXu'XL

)vru(m

ee

vvrr

rr

vv

'vru

eYcL

crLvccYL

UYLvrYUL

rvYUL

rYULrYUL

vYULvYUL

vYLrYLurvm

eee

Aovrr

vvr

rrrr

vvvv

vr

eNcL

UNLvrNUL

rvNULrNUL

rNULvNUL

vNULvNLrNLrI

eee

Aovrr

vvrrrr

rvvv

vvrz

rL vccNL +−−−+

where

[ ]crLve )2(tan 1 −−= −δ

streamdown far velocity inducedpropeller ;

streamdown far velocity inducedpropeller ;

c uRkUuRc

nDKuu

prApr

rppr AAR

diameterpropeller ;

fraction wake;

racepropeller in rudder of area projected;

rudder of area projected;

p r

velocityinducedpropeller ;

tcoefficienthrust propeller ;

UUk

SNU has conducted HPMM tests using a

model ship with a length of 6.5 m in the towing

tank whose dimension is 200 m × 14 m × 6 m.

All the tests have been carried out with fully

appended model and with the propeller operating at the ship propulsion point. Test programs are almost same with that of KRISO.

Hydrodynamic coefficients of SNU are summarized in Table 6.7. Here, all the force coefficients are taken with the origin at the ship

center of gravity.

Comparison of mathematical model and test

conditions

Mathematical models of KRISO, HSMB

and SNU are basically same. Major differences are just in representing non-linear

damping terms and propeller slip stream effects. SNU adopts cubic forms in representing

non-linear damping terms while KRISO and

HSMB adopts both square and cubic terms.

KRISO models propeller slip stream effects

simply just by introducing a ship propulsion

ratio η. HSMB and SNU use more complicated models to represent propeller slip

stream effects. They use different forms but

basic idea of their modeling is same in that

they model the velocity into the rudder based

on propeller theory.

All three organizations carried out HPMM

tests with a relatively large model and in a

sufficiently large towing tank. So we can assume that all the test results have same scale

effects and blockage effects. But HSMB performs test at the rather higher velocity than

KRISO. So this might give some differences

in force measurements due to Reynolds number effects. Test programs are very similar

except a few tests. HSMB have carried out

rudder and drift test for wider range of drift

angles while KRISO have carried out yaw and

drift test for wider range of drift angles.

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6.2. Simulations

Using the mathematical models and hydrodynamic coefficients of three organizations

described in the previous section, simulations

of maneuvering have been made for an Esso

Osaka tanker and the results are compared

with trial data.

The results of simulation for 35 degree

starboard and port turning are shown in Figures 6.1÷6.8. The agreement between trials

and simulations by three models is good.

There are some differences in yaw rate at the

early stage of turning where turning rate has a

peak value. Simulation by HSMB predicts

higher yaw rate than the trial data but simulations by KRISO and SNU underpredict. Simulation by HSMB shows higher yaw rate all the

time. HSMB predicts the smallest turning circle and SNU predicts the largest turning circle.

Predicted drift angles show very large differences. SNU predicts final drift angles as 24

degrees but KRISO as 12 degree. At present,

it is not certain which is better prediction. Although the trial data of drift angles are shown

in the figures, they are too contaminated by

current to refer.

The results of simulation for 10o/10o and

20o/20o zigzag maneuver are shown in Figures

6.9÷6.16. Generally simulations by three

models show good agreements with trial data.

Overshoot angles are well predicted although

simulation predicts a little time lagged motion. HSMB predicts much slower drop of

forward speed than trial data. But the original

simulation results made by HSMB shows

much closer results with trial data (Barr,

1993). These differences seem to be errors in

reproducing the simulations done in this

study. Contrast to turning, three models predict drift angles not so different.

To relate predicted motions with hydrodynamic coefficients, predicted forces during

maneuvering motions are examined. Figure

6.17 and Figure 6.18 show typical range of

motion variables during turning and zigzag

maneuvers respectively. A ship experiences

the largest yaw rate and drift angle at the indicated stages shown in these figures. Prediction

of hydrodynamic forces at these stages would

affect the prediction of maneuvering motions

critically. The largest motion can be observed

in the steady stage of 35 degree turning where

the speed drop ratio, the drift angle and nondimensional yaw velocity are 0.35, 18 degree

and 0.9 respectively. In the zigzag maneuver,

the largest motion can be observed at the second phase of 20o/20 o zigzag maneuver.

Figures 6.19÷6.24 show the comparison of

the predicted forces by three models over the

range of turning and zigzag maneuver shown

in Figure 6.17 and Figure 6.18. Generally the

predicted yaw moments by three models show

good agreements compared with side forces.

Over the range of typical zigzag maneuver,

three models predict almost same both side

forces and yaw moments. But predicted forces

show large differences over the range of turning motion. Especially, side forces show

much larger differences. The large differences

of drift angles seen in Figure 6.4 and Figure

6.8 are attributed to these differences.

The main cause of the difference in side

forces at the large yaw rate and large drift angle is can be found in hydrodynamic coefficients, Yvrr, Yv|r|. The values of Yvrr, Yv|r| by

KRISO are –0.03428 and 0.00321 while those

by HSMB are –0.0156 and 0.0075. There can

be many sources making this difference. The

model test conditions of KRISO and HSMB

including the size of towing tank and model,

propulsion condition and test procedure are

very similar. Just the test program for Yaw

and Drift test shows a little difference. KRISO

have carried out this test up to the drift angle

of 16 degree while HSMB up to 12 degree.

And HSMB carried out this test at the higher

speed of 0.944 m/sec while KRISO at the

lower speed of 0.504 m/sec. Analyzing

method would also affect the results. But, unfortunately, all of these cannot be confirmed

further at present because both raw model test

data are not available.

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Transfer(m)

d va n ce (m

Trial

35 deg. Starboard Turn (10.0kts)

Figure 6.1 Trajectory for 35o Starboard

turning (V = 10.0 kts).

T im e (se c)

aw

at e( d eg /s ec

T ria l

3 5 d e g . S ta rb o a rd T u rn (1 0 .0 k ts )

Figure 6.2 Time history of yaw rate for 35o

Starboard turning (V = 10.0 kts).

T im e (se c)

pe ed (k ts

T ria l

3 5 de g . S ta rbo a rd T u rn (1 0 .0 kts)

Figure 6.3 Time history of speed for 35°

Starboard turning(V = 10.0 kts).

T im e (s e c )

rif

ta n g le (d eg

3 5 d e g . S ta rb o a rd T u rn ( 1 0 .0 k ts )

Figure 6.4 Time history of drift angle for 35o

Starboard turning (V = 10.0 kts).

Transfer(m)

d va nc e( m

Trial

35 deg. Port Turn (7.7kts)

Figure 6.5 Trajectory for 35o Port turning

(V = 7.7 kts).

T im e (se c)

aw

at e( d eg /s ec

T ria l

3 5 d e g . P o rt T u rn (7 .7 kts)

Figure 6.6 Time history of yaw rate for 35o

Port turning (V = 7.7 kts).

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T im e (se c)

p ee d (k ts

T ria l

3 5 de g. P ort T urn (7 .7 kts)

Figure 6.7 Time history of speed for 35o

Port turning (V = 7.7 kts).

T im e ( s e c )

rif

ta ng le (d eg

T ria l

3 5 d e g . P o rt T u rn ( 7 .7 k ts )

Figure 6.8 Time history of drift angles for

35o Port turning (V = 7.7 kts).

T im e ( se c )

ea di n g

ng le (d eg

T ria l

1 0 - 1 0 Z ig - Z a g M a n e u v e r( 7 .5 k ts )

Figure 6.9 Time history of heading angles

for 10o/10o Zigzag maneuver (V = 7.5 kts).

T im e (s e c )

aw

at e( de g/ se c)

T ria l

1 0 -1 0 Z ig -Z a g M a n e u ve r(7 .5 k ts )

Figure 6.10 Time history of yaw rate for

10°/10° Zigzag maneuver (V = 7.5 kts).

T im e ( s e c )

p ee d (k n o ts

T ria l

1 0 - 1 0 Z ig - Z a g M a n e u v e r( 7 .5 k ts )

Figure 6.11 Time history of speed for 10o/10o

Zigzag maneuver (V = 7.5 kts).

T im e ( s e c )

rif

tA ng le (d eg

T ria l

1 0 - 1 0 Z ig - Z a g M a n e u v e r( 7 .5 k ts )

Figure 6.12 Time history of drift angles for

10°/10° Zigzag maneuver (V = 7.5 kts).

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T im e ( s e c )

ea d in g

ng le (d eg

T ria l

2 0 -2 0 Z ig -Z a g M a n e u v e r(7 .8 k ts )

Figure 6.13 Time history of heading angles

for 20°/20° Zigzag maneuver (V = 7.8 kts).

T im e ( se c)

o n d im en si o n al

aw

at e

T ria l

2 0 -2 0 Z ig -Z a g M a n e u v e r( 7 .8 k ts )

Figure 6.14 Time history of yaw rate for

20°/20° Zigzag maneuver (V = 7.8 kts).

T im e ( s e c )

p ee d (k n o ts

T ria l

2 0 - 2 0 Z ig - Z a g M a n e u v e r( 7 .8 k ts )

Figure 6.15 Time history of speed for 20°/20°

Zigzag maneuver (V = 7.8 kts).

T im e ( s e c )

ri ft

n g le (d eg

T ria l

2 0 - 2 0 Z ig - Z a g M a n e u v e r( 7 .8 k ts )

Figure 6.16 Time history of drift angles for

20o/20o Zigzag maneuver (V = 7.8 kts).

Time(sec)

aw

at e( d eg /s ec

Initial Turning Stage

starbd. turn : u'=0.8 ,δ=-35, β=12, r'=0 .6

port turn : u'=0 .8,δ=35, β=-12, r'=-0 .6

S teady Turning Stage

starbd. turn : u'=0.35,δ=-35, β=18, r'=0 .9

port turn : u'=0.35,δ=35, β=-18, r'=-0 .9

Figure 6.17 Typical values of motion variables during turning maneuver.

Time(sec)

aw

at e( de g/ se c)

1st phase

2nd phase

Figure 6.18 Typical values of motion variables during Zigzag maneuver.

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r'

35o stbd turn, initial stage

35o port turn, initial stage

Figure 6.19 Side forces at the initial turning

stage.

r'

35o stbd turn, initial stage

35o port turn, initial stage

Figure 6.20 Yaw moments at the initial turning stage.

r'

35o stbd turn,steady stage

35o port turn, steady stage

Figure 6.21 Side forces at the steady turning

stage.

r'

35o stbd turn,steady stage

35o port turn, steady stage

Figure 6.22 Yaw moments at the steady turning stage.

r'

10o/10o 1st phase

10o/10o 2nd phase

Figure 6.23 Side forces during Zigzag motions.

r'

10o/10o 1st phase

10o/10o 2nd phase

Figure 6.24 Yaw moments during Zigzag motions.

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6.3. Benchmark data based on selected

datasets of a whole ship model

As it is shown in the foregoing, the selected three datasets of a whole ship model

gives a reasonable prediction of full maneuvering performance comparable with full

scale trial data. So, their mean value of hydrodynamic coefficients can be proposed as one

of benchmark data for the study of maneuvering performance of Esso Osaka tanker.

Since three datasets are derived based on

different mathematical model and with different analyzing method, all datasets need to be

reanalyzed with same method to have same

expressional forms. To reanalyze three datasets, artificial PMM data are generated using

programs which have been used in comparative study. The ranges of generated datasets

are determined to cover the range of full scale

trials. And, new hydrodynamic coefficients of

three datasets are derived with same analyzing

method. Table 6.8 and Table 6.9 summarize

the coefficients of each dataset and mean

value of them in square form and cubic form,

respectively. Here, the mean values are obtained by analyzing all three datasets together.

The residual errors shown in tables represent

the difference of each datasets from mean

value. These errors can be, therefore, thought

as scattering of hydrodynamic coefficients

among three datasets. Hydrodynamic coefficients concerned with static drift and pure

yaw shows small scattering. But large residual

errors are observed as expected.

Using mean data in Table 6.1 and Table

6.2, prediction of full scale maneuvering performances are made and compared with trial

data. Some other data which are not shown in

tables but necessary data for simulation are

adopted from datasets of KRISO. Figures

6.13-6.16 shows the results. They show reasonable prediction but a little worse results

compared with ones shown in chapter 5.

6.4. Summary

Comparative simulation study of Esso

Osaka tanker have been done using three

datasets of deep water which were derived

based on a mathematical model of a whole

ship model. All the simulation results by three

models generally show good agreements with

full-scale trial data. But it is found that each

model shows much different prediction of hydrodynamic forces for large yaw rate and drift

angles although they predict hydrodynamic

forces almost the same over the typical motion range of turning and zigzag maneuver.

But large difference in predicting side forces

for the large yaw rate and drift angles results

in the large difference of predicting drift angles. To predict the hard maneuvering motion

which may occur either from large deflection

of rudder or the inherent instability of a ship,

more careful experimental design and analysis

of nonlinear coupling hydrodynamic coefficients are required.

As a benchmark data of hydrodynamic

coefficients for whole ship model, mean data

of three datasets are suggested. Simulated

results using benchmark data show reasonable

prediction but a little worse results compared

with ones shown in chapter 5.

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Table 6.8 Summary of Hydrodynamic Coefficients for Benchmark data (square form).

Coeffs. KRISO HSMB SNU Mean

Rresidual

(r.m.s)

Residual

(max)

Relative

Error(r.m.s)

Table 6.9 Summary of Hydrodynamic Coefficients for Benchmark data (cubic form).

Coeffs. KRISO HSMB SNU Mean

Residual

(r.m.s)

Residual

(max.)

Relative

Error(r.m.s)

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Esso Osaka Specialist Committee in 23rd

ITTC was requested to discuss the proposed

data estimated by captive model test and to

propose the benchmark data. Committee discussed the reasons of scattering in proposed

data and decided to study the data that we can

know the detail experimental and analyzing

procedures. Committee made several studies

based on simulation on trial and free running

model test. Finally, committee proposed the

benchmark data relating to 2 kinds of mathematical model.

Esso Osaka trial data include some results

in shallow water condition. Committee tried

to discuss the data, but we could not get sufficient data by mean of insufficient information

on experiments and analyzing procedures. Finally, committee concluded to discuss the issues in deep water condition.

For benchmark data the conclusions are:

MMG model

The hydrodynamic forces proposed by different institutes show little difference from

view point of comparing the scattering in results of free running model test. Therefore, we

propose to use the mean data as defines

herein, as a benchmark data set for hydrodynamic coefficients. We cannot make enough

discussion on the forces concerning propeller

and rudder because we can correct small number of them. However, as the estimated results

show good agreement to the results of free

running model tests, we propose the data

shown in this paper as benchmark corresponding to individual mathematical model.

Whole Ship model

The mean value of hydrodynamic coefficients

of three selected data sets, summarized in Table 6.8 and Table 6.9 at chapter 6, are proposed as a benchmark data for the study of

maneuvering performance of Esso Osaka

tanker for a mathematical model with whole

ship model type. On the propeller-rudder interaction model, there might be some arguments but KRISO model is proposed because

it is simpler.

Abkowitz, M.A., 1984, “Measurement of Ship

Hydrodynamic Coefficients in Maneuvering from Simple Trials During Regular

Operation”, Massachusetts Institute of

Technology Report MIT-OE-84-1.

Barr, R., 1993, “A Review and Comparison of

Ship Maneuvering Simulation Methods”,

Transactions of the SNAME, Vol. 101.

Crane, C.L., jr., 1979a, “Maneuvering Trials

of the 278,000 DWT Esso Osaka in Shallow and Deep Water”, Transactions of the

SNAME, Vol. 87, pp. 251-283.

Crane, C.L., Jr., 1979b, “Maneuvering Trials

of the 278,000 DWT Esso Osaka in Shallow and Deep Water”, Exxon International

Company Report EII.4TM.79.

Dand, I.W., and Hood, D.B., 1983 “Maneuvering Experiments Using Two Geosims

of the Esso Osaka”, National Maritime

Institute (NMI) Report No. NMI R168.

Hydronautics, 1980, “Model Test and Simulation Correlation Study Based on the Full

Scale ESSO OSAKA Maneuvering Data”,

Hydronautics report No. 8007-1.

Kim, S.Y., 1988, “Development of Maneuverability Prediction Technique”, KIMM Report No. UCE.337-1082.D.

MMG, 1985, “Prediction of Manoeuvrability

of A Ship”, Bulletin of the Society of Naval Architects of Japan, Published by The

Society of Naval Architects of Japan.

Rhee, K.P., Ann, S.P., Ryu, M.C., 1993,

“Evaluation of Hydrodynamic Derivatives

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Proceedings of the 23rd ITTC – Volume II 617

from PMM Test by System Identification”,

Proceedings of MARSIM ’93.

Roseman, D.P., Editor, 1987, “The MARAD

Systematic Series of Full-Form Ship Models”, Published by the SNAME, New

York, NY, USA.

Webster, W.C., Editor, 1992, “Shiphandling

Simulation − Application to Waterway Design”, Published by the National Academy

Press, Washington, DC, USA.

Yoshimura, Y., 2001, “A study on Hydrodynamic derivatives and interaction coefficients”, Maneuverability Prediction Group

2001, Report No. Map 8-5.

23rd International

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Proceedings of the 23rd ITTC – Volume III 739

I.1. Discussion on the Report of the 23rd

ITTC Specialist Committee on Esso

Osaka: Manoeuvring in shallow

water

By: Masayoshi Hirano, Mitsui Akishima

Laboratory, Japan

First of all, as a member of former ITTC

Manoeuvring Committee, I would like to congratulate the committee on this fine report.

The committee members must have done very

laborious work. I would like to make a couple

of comments as follows.

1. Theoretical approach

Nowadays CFD technique has greatly

been improved and practical applications are

widely being attempted not only in the area of

resistance and propulsion but also in other

area such as manoeuvring. Such an advanced

technique as CFD may be needed to develop

the benchmark data with more reliability.

2. Manoeuvring in shallow water

From the view point of manoeuvring

safety, ship behaviour in shallow water area is

much more important than in deep water. Although there may not exist sufficient information for Esso Osaka, efforts for the benchmark

in shallow water should be continued by employing such a way as theoretical approach

mentioned above.

I.2. Discussion on the Report of the 23rd

ITTC Specialist Committee on Esso

Osaka: Selection of data sets

By: Marc Vantorre, Ghent University, Belgium, Flanders Hydraulics Research, Antwerp, Belgium

In the first place I would like to congratulate the Specialist Committee with the final

results. The task, which was based on a recommendation formulated by the 22nd ITTC

Manoeuvring Committee, was not an easy one,

taking account of the large scatter in existing data

and the fact that most tests were carried out decades ago. If time allows, I have several questions I

would like to discuss, some of them directly

related to the report, other being of a more

general character.

Reason of data scatter

It was clear that it was an impossible task

to explain the very large differences between

the experimental data sets. A list of potential

sources of errors was given in Chapter 3.

Most of these sources are also mentioned in

the Manoeuvring Captive Model Test Procedure; I would like to suggest to the next Manoeuvring Committee to check whether additional elements mentioned in the Report of the

Esso Osaka Specialist Committee should be

incorporated into the Procedure. I assume the

Committee will agree that it would have been

much easier to identify the sources of scatter

if the tests had been documented in a way

suggested by the Procedure; please consider

The Specialist Committee on

Esso Osaka

Committee Chair: Prof. Hiroaki Kobayashi (Tokyo Univ. Mercantile Marine)

Session Chair: Dr. Georges Thiery (Bassin d’Essais des Carènes)

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this as a strong promotion for a proper captive

model test documentation system.

It would be useful to have some more detailed explanation with Figure 3.1.

Selection of data sets

In Chapter 2 it is described in which way

data sets were eliminated so that only five remaining sets for both sway force and yaw moment were left. It is not clear whether the four

sets of tests mentioned in Section 5.2 and in

Table 5.1 have any relation with these five remaining sets; some additional information

would be appreciated. If they have, some questions about the reputation of PMM yawing tests

could be raised, as the four data sets in Table

5.1 are obtained by circular motion tests.

Sources of scatter are more numerous in the

case of PMM testing, as the number of test parameters to be selected is larger and nonstationary techniques are used for investigating

quasi-steady phenomena. As the selection of

the test parameters is even more important for

the reliability of PMM tests, an adequate

documentation of the test conditions is, especially for this type of tests, absolutely required.

It should also be mentioned that the first,

“mechanical” generations of PMM systems

were in some cases not able to generate a purely

harmonic yaw motion without inducing drift.

Moreover, only small amplitude motions could

be generated with the first PMM systems, so that

a sufficiently large range of yaw rates could only

be obtained by increasing the PMM frequency.

More recent larger amplitude PMM systems can

only generate purely harmonic yawing motions

if the main carriage speed can be varied during

the test, and if the sway carriage is able to perform non-harmonic motions. If this is not the

case, fluctuations of the longitudinal ship speed

and drift will be induced, and the forces and

moments caused by these parasitic motions will

affect the test results.

Most of these kinematics problems can be

overcome by the use of CPMC type facilities,

if properly controlled.

Shallow water data

One of the primary advantages of the selection of the Esso Osaka for benchmark data

was the availability of trial data at reduced

water depth. Although I fully understand that

the Committee confined its task to deep water

data, this aspect being hard enough already, it

can be regretted that the shallow water trial

data have not been incorporated in the

benchmark data. Therefore, I would like to

ask the Committee’s opinion about a possible

extension of its work to the shallow water

case.

An analysis of available shallow water

data can be expected to be still more difficult.

The number of data sets is not only considerably smaller, and the scatter is certainly not

less, as is illustrated in Figures I.2.1 and I.2.2.

Moreover, in many cases shallow water data

are only available in a format based on the

deep water data. Some sources of scatter are

amplified in shallow water: as an example, the

effect of propulsion on lateral force and yawing moment is much more important in shallow water (Figure I.2.3).

Unified data

In order to compare the four sets of hydrodynamic hull force data in Chapter 5, unified

data were calculated, i.e. instead of comparing

the manoeuvring coefficients, nondimensional forces and moments were calculated for a number of combinations of sway

and yaw velocities. I fully agree that such a

tabular way of presenting results is often

much more useful than a set of coefficients,

especially when the range of validity is not

specified. Therefore, I would like to suggest

promoting this methodology in either the Captive Model Test Procedure or the Validation

of Simulation Models Procedure.

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Drift angle (deg)

VBD, Duisburg, regression model

WLH, Antwerp, tabular model

BSHC, Varna, regression model

Maximum angle β of model tests:

VBD, [-24deg; 24deg]

BSHC, [-20deg; 8deg], for Fn = 0.0655

WLH, [-180deg; 180 deg]

Drift angle (deg)

VBD, Duisburg, regression model

WLH, Antwerp, tabular model

BSHC, Varna, regression model

Maximum angle β of model tests:

VBD, [-24deg; 24deg]

BSHC, [-20deg; 8deg], for Fn = 0.0655

WLH, [-180deg; 180 deg]

Figure I.2.1. Esso Osaka, h/T = 1.20: Non-dimensional lateral force and yawing moment due to drift.

742 The Specialist Committee on Esso Osaka

23rd International

Towing Tank

Conference

γ angle (deg)

VBD, Duisburg, regression model

BSHC, Varna, regression model

WLH, Antwerp, tabular model, Fn=0.033

WLH, Antwerp, tabular model, Fn=0.049

WLH, Antwerp, tabular model, Fn=0.066

Maximum angle γ:

VBD, Duisburg, 15 deg

BSHC, Varna, 15 deg

WLH, Antwerp, 50 deg

γ angle (deg)

VBD, Duisburg, regression model

BSHC, Varna, regression model

WLH, Antwerp, tabular model, Fn=0.033

WLH, Antwerp, tabular model, Fn=0.049

WLH, Antwerp, tabular model, Fn=0.066

Maximum angle γ:

VBD, Duisburg, 15 deg

BSHC, Varna, 15 deg

WLH, Antwerp, 50 deg

Figure I.2.2. Esso Osaka, h/T = 1.20: Non-dimensional lateral force and yawing moment due to yaw.

23rd International

Towing Tank

Conference

Proceedings of the 23rd ITTC – Volume III 743

drift angle (deg)

n = 0

n = 0.6 nmax

n = 1.0 nmax

Figure I.2.3. Esso Osaka, h/T = 1.20: Non-dimensional lateral force due to drift, effect of propeller rate (Flanders Hydraulics, Antwerp).

II.1. Reply of the 23rd ITTC Specialist

Committee on Esso Osaka to M.

Hirano

No reply by the Committee.

II.2. Reply of the 23rd ITTC Specialist

Committee on Esso Osaka to M.

Vantorre

No reply by the Committee.

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