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CAPTIVE MANOEUVRING TESTS WITH SHIP MODELS: A REVIEW OF ACTUAL
PRACTICE, BASED ON THE
22ND ITTC MANOEUVRING COMMITTEE QUESTIONNAIRE
Mare Vantorre, University o f Ghent (Department o f Marine
Technology), Ghent, Belgiumc/o Flanders Hydraulics, Antwerp,
Belgium
Introduction
Captive model test techniques are nowadays commonly used for
predicting ship manoeuvring characteristics. A distinction is made
between different types of captive tests:(a) stationary straight
line tests, which can be carried out in a towing tank;(b) harmonic
tests, requiring a towing tank equipped with a planar motion
mechanism;(c) stationary circular tests, performed by means of a
rotating arm or a x-y carriage in a wide basin.
Harmonic tests (b) were introduced about 40 years ago; the other
types are a few decades older. Taking account of the large number
of test parameters to be selected and the differences between and
evolution of the concepts of the existing mechanisms, at present
each institution applies its own test methodology, mainly based on
its own experience and semi-empirical considerations.
The International Towing Tank Conference (ITTC) identified an
increasing need for guidelines and even standard test procedures
for the execution of this type of ship model tests, in order to
ensure the quality of the experimental results. The 22nd ITTC
Manoeuvring Committee considered a thorough insight in present
methodologies for selecting the experimental parameters for captive
model tests, being the result of years of experience of many
institutions, as a requirement. For this reason, a questionnaire
was circulated among 110 ITTC Member Organisations.
Thanks to the satisfactory response, the Captive Model Test
Procedure, formulated by the 22nd ITTC Manoeuvring Committee and
published in the ITTC Quality Manual in 1999 (Ref. 1), could be
provided with quantitative data reflecting the present
state-of-the-art.
A summary of the responses to the questionnaire was given in the
Report of the Manoeuvring Committee at the 22nd ITTC (Ref. 2). The
present paper provides a more detailed overview of actual practice
concerning captive manoeuvring tests.
The Questionnaire
The questionnaire consisted of three parts.In part 1,
Experimental facilities: main specifications and physical
limitations, details were
asked about tank dimensions, ranges of mechanism kinematics and
the range of model dimensions.In the second part, entitled
Experimental program: actual practice, information was asked
about the number of values and the ranges of the parameters
determining the captive model test program. Generally, distinction
can be made between three kinds of parameters:
Kinematic parameters, determining the velocity and acceleration
components of thedriving mechanism and, hence, the ship model;
Ship control parameters, in most cases limited to propeller rate
and rudder angle; Operation and analysis parameters, which may
affect accuracy and validity of test
results (e.g. measuring time, number of PMM cycles, waiting time
between runs).Part 3 requested for information about Data
acquisition and processing.
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A positive and useful answer was received from 37 institutions,
covering 58 facilities distributed as shown in Table 1. It can be
concluded that a majority of the institutions performing captive
manoeuvring tests are able to combine stationary straight-line
tests (a) with harmonic tests (b). Facilities for circular motion
tests (c) are rather scarce, and it should be mentioned that some
of the institutions only seldom make use of it. This is especially
the case for rotating arm facilities; recently built facilities for
circular motion tests are always wide tanks equipped with a x-y-vy
carriage.
Table 1. Number of Facilities and Institutions.(a) only (b) only
(c) only (a)+(b)
not(c)(a)+(c) not(b)
(b)+(c) not(a)
(a)+(b)+(c)
total
# facilities 14 - 7 31 2 - 4 58# institutions 3 - 1 23 3 - 7
37
Part 1. Experimental Facilities
Tank DimensionsDistributions of the main dimensions (length,
width, depth, length to width ratio) of the tanks
used for the three types of captive model tests are displayed in
figure 1. The distributions for tests (a) and (b) are very similar,
which could be expected as most facilities are able to perform both
types.
Mechanism KinematicsFacilities for executing tests of type (a)
are typically towing tanks equipped with a model
connection system allowing measurement of horizontal forces and
moments and setting of drift angles. Distributions of the maximum
drift angle are displayed in figure 2(a); 60% of the facilities
have no restrictions regarding the static drift angle.
Figure 3 gives an overview of the maximum sway (yA) and yaw
(\yA) amplitudes of PMM systems used for executing harmonic tests
(b). A clear distinction can be made between PMM systems with
restricted amplitude ranges, mostly driven by one single motor, and
mechanisms with three degrees of freedom, which are mostly computer
controlled: about one third of the facilities appear to be equipped
with a (large amplitude) x-y-vy carriage. Figure 2(b) concerns the
maximum static drift angle.
Model DimensionsFigure 4 presents differential and cumulative
distributions of the data obtained on ship model
length. As some answers referred to a range of lengths, while
others only gave an average value, it was presumed that for the
latter the minimum and maximum values were 33% lower and higher
than the mean value, respectively. For test types (a/b), the median
value for the model length appears to be 4.5 m, while the
distribution reaches a peak at a length of 3.0 m; 95% of all tests
are carried out with model length L > 2 m. On the average,
circular tests (c) are performed with smaller models: the median
length is only 3 m, the peak in the distribution is reached at 2.2
m, and the 95% limit is 1.5 m.
Distributions of ratios of model length to tank dimensions are
displayed in figure 5. Most tests (a/b) are carried out in a tank
with a length of 35 times the model length L, while the largest
dimension of tanks for circular tests (c) is typically 20 L. The
median value for the model length to tank width ratio L/W is 0.47
for stationary straight-line tests (a); it is somewhat smaller
(0.42) for harmonic tests(b), as PMMs are usually mounted in tanks
that are wider than the average towing tank. Tests (c) are executed
in circular or wide tanks, leading to a much smaller median L/W
(0.09).
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Part 2(a). Experimental Program: Stationary Straight Line
Tests
Test TypesAmong tests of type (a), stationary straight-line
tests, distinction can be made between:(al) straight towing;(a2)
straight towing with rudder deflection;(a3) oblique towing;(a4 )
oblique towing with rudder deflection.
Kinematic and Ship Control ParametersStationary straight-line
test conditions are characterised by following parameters:
kinematic parameters: ship model (or carriage) speed, drift angle
(only for a3, a4); ship control parameters: propeller rate, rudder
angle (only for a2, a4);The questionnaire asked for information
about the usual number of values and the way of
selecting the values. The response is summarised in figures
6-11, leading to following conclusions: The number of forward
speeds depends on the test type (figure 6), although the
highest
frequency of occurrence is obtained for only one speed. On the
average, more speeds are selected for resistance-propulsion tests
(al), as the self-propulsion point has to be determined by this
kind of tests. For a2/a3/a4, the median value appears to be 1 or
2.
The majority of the tests is carried out at only one propeller
rate (see figure 7), being the (model or ship) self-propulsion
point. Straight towing tests without rudder action (al) and rudder
force tests (a2) are often carried out at other propeller loading
as well.
The number of drift angles applied in tests a3-a4 is on the
average smaller for oblique towing tests with rudder action (see
figure 8). The highest frequency is observed at 12 angles for type
(a3), and 5 angles for type (a4). A similar distribution is
obtained for the number of rudder angles at which tests a2/a4 are
carried out (see figure 9). The way drift and rudder angles are
selected is displayed in figures 10 and 11, respectively.
Operational and Analysis Parameters.Following operation and
analysis parameters are considered for tests of type (a): waiting
time
between runs, length of acceleration phase, settling phase,
steady phase and deceleration phase.An overview of the response is
given in Figure 12. Mostly, no distinction is made between the
different types of tests. On the other hand, the length of the
steady phase may influence the accuracy of the analysis results;
according to Ref. 9, a measuring length of three times the ship
model length should be considered as a minimum. Obviously, this
condition is fulfilled by a majority of the test runs.
Part 2(b). Experimental Program: Harmonic Tests
General ConsiderationsFollowing tests of type (b), harmonic
tests to be performed in a towing tank equipped with a
planar motion mechanism, are considered:(b 1 ) pure sway tests
;(b2) pure yaw tests;(b3) yaw tests with rudder deflection;(b4) yaw
tests with drift.Compared to straight-line tests (a), the number of
parameters is considerably larger.
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Kinematic and Ship Control Parameters: OverviewThe models
kinematics during a test of type (b) is determined by following
parameters: the ship models forward velocity component u; for tests
(bl): the lateral motion amplitude yoA and oscillation frequency
to, determining
the sway velocity amplitude va and sway acceleration amplitude
VA :
v A =yoAc ; * A = y 0A2 ( la)or, expressed in a non-dimensional
way:
_ VA yOA L , , . , _ VAL y 0A co2 L2 _ , ,2A = -------=
;------------ = yOAw l VA = 9 - yO A w l ( l b )
u L u u 2 L u 2 for tests (b2,b3,b4): the yaw amplitude \\ia and
oscillation frequency to, determining the
yaw velocity amplitude rA and yaw acceleration amplitude f A
:
rA = M7a - ; fA = ^ Ato2 (2a)u uor, non-dimensionally:
2
*A s = a 1 y '0 A i2 ; *A = T r = V A ',2 * y'oA'l3 (2b)U u
2
The approximations are valid for small yaw amplitudes, and
illustrate the indirectinfluence of the lateral amplitude;
for tests (b4): the drift angle .Ship control parameters applied
during harmonic tests are usually the propeller rate n and, for
tests (b3), the rudder angle .
Forward SpeedThe number of forward speeds u applied during a
harmonic test program is displayed in Figure
13. For a large range of applications, only one forward speed
value is selected.
Sway and Yaw Velocity AmplitudeThe number of sway and yaw
velocity amplitudes applied during test programs of types (bl)
and (b2), respectively, is displayed in figure 14. This number
varies between 1 and 20, 4 being a median value. There is only a
slight difference between the distributions for sway and yaw tests,
which is remarkable, as generally tests of type (bl) are only
carried out for determining the sway acceleration derivatives,
while tests (b2 ) also provide data on both yaw rate and yaw
acceleration dependent forces and moments. As shown in figure 15,
median ranges for non-dimensional sway and yaw velocity amplitudes
are [0.1 ; 0.35] and [0.16 ; 0.58], respectively.
As stated above, a sway/yaw velocity amplitude is the result of
a combination of sway/yaw amplitude and oscillation frequency.
Sway and Yaw AmplitudeThe number of amplitudes applied in a
harmonic sway/yaw test program varies between 1 and
10, 3 being a median value (see figure 16).The lateral amplitude
yoA may be restricted due to technical limitations of the
driving
mechanism, but even if the lateral motion extends over the full
tank width, interference of the model with the tank walls should be
avoided. Figure 17 shows that the lateral amplitude typically takes
less
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than 10% of the tank width, and that in more than 90% of the
cases the swept path does not exceed half the tank width, as
recommended in Ref. 3. Concerning harmonic yawing tests, only a
limited number of completed questionnaires contained a range of yaw
amplitudes, varying between 5 and 35 deg; also for this kind of
tests, restrictions to lateral motion appear to be of greater
importance.
PMM Oscillation FrequencyThe median number of frequencies
selected for PMM tests is 2, as illustrated in figure 18; many
test programs are based on one single value for the test
frequency only.For the selection of the values of these
frequencies, several authors formulated guidelines based
on non-dimensional expressions for to :
tests lead to compromise values for toi' which are in the range
mentioned above for yaw tests (2-4), but which are very low
(0.25-2) for sway tests. If sway velocity derivatives are
determined by oblique towing, the accuracy of the inertia terms can
be improved by increasing the test frequency (Refs. 1 and 9)
Restrictions for 0)2' can be interpreted as measures for
avoiding tank resonance. If the PMM frequency equals one of the
natural frequencies of the water in the tank, a standing wave
system may interfere with the tests. This occurs if the wave length
of the wave system induced by the oscillation equals 2W/n (n = 1,2,
...), W being the tank width. In case of infinite depth, the lowest
natural frequency (n=l) occurs at to2' = 7iL/W.
Restrictions for 0)3' are imposed for avoiding unrealistic
combinations of pulsation and translation; 0)3' should be
considerably less than 0.25 during PMM tests (Refs 3, 5 and
10).
In order to compare common practice with these guidelines, the
questionnaire requested to specify the method applied for selecting
frequencies; unfortunately, only a minority of the answers appeared
to be based on non-dimensional values (1 based on toi', 2 on (02',
1 on (03'). In order to convert the responses to non-dimensional
values, a Froude number range between 0.05 and 0.3 was assumed
unless specified otherwise. The results are summarised in figure
19.
Interaction of yawing with drift (b4) is typically verified at
four drift angles, selected in the range between -30 and +30 deg;
[0 deg ; 16 deg] appears to be a median range (see figure 20).
Ship Control ParametersHarmonic tests are usually carried out at
only one propeller rate (see figure 21), the self-
(3)
Obviously, limitations of toi' are overruled by those of 102' or
103' for larger Froude numbers. Restrictions of toi' can be
interpreted as follows. Restriction of the number of oscillation
cycles c due to the available tank length Ltank:
(4)
Several authors (Refs 4-7) suggest maximum values for toi' to
avoid non-stationary lift and memory effects; typical values are
1-2 for sway and 2-3 for yaw tests. Comparablevalues result from
considerations on lateral wake patterns (Ref. 8).
Considerations on the accuracy of the hydrodynamic derivatives
determined by PMM
Drift Angles
propulsion point of the ship or the model. Interaction of yawing
with rudder action (b3) is typically
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verified at three rudder deviations. No tendency can be observed
concerning the selection of the range of rudder angles (see figure
22 ).
Operational and Analysis Parameters.Following parameters do not
influence the ships kinematics, but may affect the test results:
length of acceleration phase; length (number of cycles) of
transient phase; length (number of cycles) of steady phase; length
of deceleration phase; waiting time between two runs; number of
harmonics considered during analysis.The length of acceleration and
deceleration phase is not selected significantly different
compared to stationary straight-line tests. Figure 23 displays
the number of cycles skipped in order to obtain a steady state
(usually 1 cycle), and the number of cycles considered for analysis
(usually 2-3 cycles). Waiting times between tests of types (a) and
(b) are comparable (usually 10 to 20 min).
Part 2(c). Experimental Program: Stationary Circular Tests
Test TypesAmong tests of type (c), stationary circular tests,
distinction can be made between:(cl) pure yawing;(c2) pure yawing
with drift;(c3) pure yawing with rudder action.
Kinematic and Ship Control ParametersSuch tests are determined
by following parameters: kinematic parameters: ship model forward
speed, yawing rate, drift angle (c2 only); ship control parameters:
propeller rate, rudder angle (c3 only).Distributions of the number
of values selected for these parameters are shown in figure 24.
Due
to the limited number of responses for this test type, no
figures concerning the range of these parameters were produced.
Following conclusions could be drawn.
Most tests are carried out at only one combination of forward
speed and propeller rate. The number of yaw rates varies from 2 to
16, with 4 as a median value. The non-
dimensional values r=rL/u vary from 0.07 to 1, the median range
being [0.2 ; 0.75]. Interaction between yaw and drift is evaluated
at a number of drift angles varying from
3 to 24, 7 being the median value. The maximum drift angle
varies between 10 and 20 deg; an asymmetric range is applied by
about 50% of the respondents.
Important spreading is observed concerning the number and range
of rudder angles.
Operational and Analysis Parameters:Following parameters are of
interest for tests of type (c): waiting time between runs, usually
chosen between 10 and 20 minutes (figure 24); length of
acceleration, settling, steady and deceleration phases. The number
of responses
was very limited; it can be concluded that only a limited
fraction of a revolution, typically less than 180 deg, can be used
for analysis, as 120 to 180 deg are required for accelerating and
about 60 deg for settling.
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Part 3. Data Acquisition and Processing
The respondents were asked which data are always, sometimes or
never measured during captive manoeuvring tests. Distinction is
made between data concerning the dynamics and kinematics of the
ship model, control parameters of the ship model, and control
parameters of the mechanism.
The replies are reflected in figure 25, and can be summarised as
follows: Hull forces in the horizontal plane are, obviously, always
measured. A majority of the respondents always measures following
data:
> position and/or speed of driving mechanism;> ship model
control settings (rudder angle, propeller rate);> propeller
thrust and torque.
A majority of the respondents always or sometimes measures
following data:> rolling moment;> rudder forces and
moments;> vertical ship motions.
Calibrations are typically carried out before and after a new
test program.Sampling rates vary between 4 and 250 Hz, 20 Hz being
a median value.
Concluding Remarks
The analysis of the replies to the 22nd ITTC Manoeuvring
Committee Questionnaire provides a thorough insight into the
present state-of-the-art concerning the methodology for execution
of captive manoeuvring tests. Thanks to the satisfactory response
and the detailed answers, to be considered as a summary of the
experience that has been developed in a large number of institutes
for several decades, a solid base was provided for this
analysis.
On the other hand, these data and their analysis should be
considered with some caution, especially if it is applied as a tool
for developing a standard captive model test procedure. Indeed,
such a procedure should always take account of the specific
conditions determined by:
the characteristics of the experimental facility (e.g. tank and
model dimensions, type of PMM facility, range of mechanism
kinematics), which may imply restrictions to the selection of test
parameters, and result into facility dependent 'optimal' test
programs and procedures;
the application domain of the test results, which may require
different ranges of test parameters to be investigated (e.g.
determining linear manoeuvring derivatives for evaluating the
course stability, mathematical model for prediction of standard
manoeuvres, input for simulator models including harbour
manoeuvring).
The latter explains the large variation in the number and range
of selected values of some of the parameters, e.g. drift angles,
rudder deflections, forward speeds.
Furthermore, it should be emphasised that test procedures need
to be updated permanently; common practice is not necessarily equal
to optimal practice. In this respect, it is important to keep in
mind the philosophy on which parameter selection criteria are
based. Sometimes it was impossible to retrieve this philosophy in
the answers to the questionnaire. As a typical example, the
selection of PMM frequencies for harmonic tests (b) could be
mentioned:
Although harmonic test results used for quasi-stationary
purposes should be checked on their frequency dependency, only one
frequency is applied in 50% of the test programs.
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In a majority of the completed questionnaires, oscillation
frequencies were expressed in absolute figures. Only a few
respondents made reference to selection criteria based on
non-dimensional values, as recommended by existing guidelines.
Moreover, it was shown that the parameter choice often does not
follow these guidelines (see figure 19).
Captive model experiments are considered as a major tool in ship
manoeuvring research, and will keep fulfilling an important role in
determining mathematical simulation models and providing data for
validation of numerical calculation methods. Therefore, test
procedures should be based on a set of guidelines in order to
ensure the quality and reliability of the test results. If handled
with caution, the results of the Questionnaire may provide
quantitative data for such guidelines.
Acknowledgements
The questionnaire on captive manoeuvring experiments was carried
out in the frame of the tasks of the 22nd ITTC Manoeuvring
Committee. The author would like to thank all members for their
support: Dr. S. Cordier (chairman), Dr. R. Barr (secretary), Dr. G.
Capurro, Dr. M. Hirano, Dr. J. Buus Petersen, Prof. K.-P. Rhee,
Prof. Zou Z.-J.
On behalf of the Committee, the author would like to express his
appreciation to all ITTC Member Organisations that have completed
the questionnaire.
References
1. "Manoeuvring - Captive Model Test Procedure" (1999). 22nd
International Towing Tank Conference, ITTC Quality Manual,
4.9-03-04-03, 25 pp. Seoul, Korea & Shanghai, China.
2. "Report of the Manoeuvring Committee" (1999). 22nd
International Towing Tank Conference, Proceedings, Volume I, pp.
71-118. Seoul, Korea & Shanghai, China.
3. Leeuwen, G. van (1964), "The lateral damping and added mass
of an oscillating shipmodel", Shipbuilding Laboratory,
Technological University Delft, Publication No. 23.
4. Nomoto, K. (1975), "Ship response in directional control
taking account of frequency dependent hydrodynamic derivatives",
Proceedings o f the 14th ITTC, Ottawa, Canada, Vol. 2,
p.408-413.
5. Wagner Smitt, L. and Chislett, M.S. (1974), "Large amplitude
PMM tests and maneuvering predictions for a Mariner class vessel",
10th Symposium on Naval Hydrodynamics, Boston, USA, pp.
131-157.
6 . Milanov, E. (1984) "On the use of quasisteady PMM-test
results", International Symposium on Ship Techniques, Rostock,
Germany
7. Leeuwen, G. van, 1969, "Some problems concerning the design
of a horizontal oscillator" (in Dutch), Shipbuilding Laboratory,
Technological University Delft, Report No. 225.
8 . Vantorre, M. and Eloot, K. (1997), "Requirements for
standard harmonic captive manoeuvring tests", MCMC'97, Brijuni,
Croatia, pp. 93-98.
9. Vantorre, M. (1992), "Accuracy and optimization of captive
ship model tests", 5thInternational Symposium on Practical Design o
f Ships and Mobile Units, Newcastle uponTyne, UK, Vol. 1, pp.
1.190-1.203.
10. Goodman, A., Gertler, M. and Kohl, R. (1976), "Experimental
technique and methods ofanalysis used at Hydronautics for
surface-ship maneuvering predictions", 11th Symposium on Naval
Hydrodynamics, London, UK, pp. 55-113.
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diff.
dist
ribu
tion
(-)
diff.
dist
ribut
ion
(-) 0.02
0.01
0.00
... .......................
J l /I
J U r 1 W -1 ^ 1
i F
1
0.83co
0.6 ?.-9
0.4 .2
0.2 1
100 200 300tank length (m)
400
0.50
0.30
0.20
0.10
0.000 10 20 30
1
0.83co
0.6 ?
0.4 .2
0.2 1 O0
0.50
3 0 . 4 0c
1 0.30
I 0.20
0.00
0.10
I'w ' (*0T 0.06
.2 0.04T3
0 .6 ''Sx0.4.
ig 0.02 0.2
0.000 20 40 60 80
tank width (m)
jr / ,
"------
T 1t - - 3 -
J0
0 2 4 6tank depth (m)
8tank length / tank width (-)
Figure 1. Main facility dimensions: differential and cumulative
distributions.
090 (deg) 1800
0.1
73
0
(b)
i. io0 90 (deg) 180
Figure 2. Facilities for test types (a) and (b): distributions
of maximum static drift angle
5 yA(m)l0 15 0.5 2yA/W (-)
0.05
73
J. J90^A (deg) 180
Figure 3. Facilities for test type (b): distributions o f
maximum amplitudes.
429
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0.5
0.8
0.60.3
0.2 0.4
0.2
0 105 15
c0'SX1 T3
ship model length (m)
Figure 4. Distributions of the length of ship models used for
several types of captive model tests.
c_oSX'Bto-3
i
0.8
0.6 0.6 S
0.4 0.4 :
0.2 0.2 3
00 0.1 0.2
0.6 a
0.4 .2
0 0.2 0.4 0.6 0.8ship model length / tank width
1ship model length / tank length
Figure 5. Distributions of the ratios of ship model length to
tank length and to tank width.
0 . 4
Q o
0 . 4
1 G1 o o 0.5
0.8 J l 0 .4J3
0.6 1 disi O U)
-
Diff
eren
tial
distr
ibut
ion
Diff
eren
tial
distr
ibut
ion
0 .40.8 0.8 0 .40.60.6 a
0.2 3
0 O
30.8 3 0.8 0.8 0.80.6 0.6 a
0.2 3
2 3 4 5 6 7 8 9 10 Number of propeller rates
2 3 4 5 6 7 8 9 10 Number of propeller rates
Figure 7. Stationary straight line tests: distribution of the
number of propeller rates
0.25
0.8 0.2 0.8 x>0.6
0.4
ju 0.05ta
^ r-* oNumber of drift angles
Figure 8. Stationary straight line tests: distribution of the
number of drift angles.Number of drift angles
0.8 J 0.25
js 0.2
3 0.15
B o.ic
-
oOn ON i/> l/> NO OO1 drift angle (deg)
0.5
O
-..........I
i t i y. ^^99P
................... A
J I *
W M i r > i r > i r > i r > i r > i r > o o '
O i n r i N O O ' ^ ' O ' r i ^' T ' T "T ' T V ' T ' ' ' drift
angle (deg)
io
i n o i n o i n o i n o i n o i n o r ^ i T f ' O t ' - O v O f
N r ^ i i n ' O O O
Figure 10. Distributions of limits of drift angle range applied
for stationary straight-line tests
0.5
-40 -30 -20 -10 0 10 20 30rudder angle (deg)
40
Go3X
T3
iti3
7 -+-+-+(a4) 1 1 I X, - J y
. ! ^- H H
lc.23XIT3Io0
-40 -30 -20 -10 0 10 20 30 40rudder angle (deg)
Figure 11. Distributions of limits of rudder angle range applied
for stationary straight-line tests.
0.2
T3
0 100 5
1
acc. dist. / model length (-) settling dist. / model length
co'SX
MT313
T3
i50
0 10 20 30steady dist. / model length
Figure 12. Stationary straight line tests: distributions of
operation and analysis parameters
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0.5co
o
0 10 20 30 40 50100 5decel. dist. / model length W aiting tim e
(min)
Figure 12 (cont). Stationary straight line tests: distributions
of operation and analysis parameterss o 1!... 06
3 0.4 0.2
teS o
Q 0.0
blu1 _ _1 2 3 4 5 6 7 8 9 10
0.80. 6 s
0.8 x>0.8 0.8 r9
0.6 ^
0.2 2
0 U0 U
0.8 -2 0.80.8 -g
0.2 3 0.2 2
0 U 0 u
Number of forward speeds1 2 3 4 5 6 7 8 9 10
Number of forward speedsFigure 13. Harmonic tests: distribution
of the number of forward speeds.
1 3 5 7 9 11 13 15 17 19Number of sway velocities
3 5 7 9 11 13 15 17 19Number of yaw velocities
Figure 14. Harmonic tests: distribution of the number of
sway/yaw velocities
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lower limit
upper limit
(bl)
10.50
lower limit
upper limit
(b2)
0 2Figure 15. Harmonic tests: distribution of non-dimensional
sway/yaw velocity amplitude range.
o 0.5
-
0.2 1 2.5
Vi Vi
0 0
10
10 (O1! 20 co2 0. 4 3
Figure 19. Harmonic tests: distributions of non-dimensional
oscillation frequencies, with indication ofempirical
guidelines.
s i .2.>0.8
3 0.6
I 0. 4 c
-
I 0.6 I 0.4
z
2 3 4 5 6 7 9 10
0.8 0.6
_ _ b3 " , , ~
y .. / _-40 -30 -20 -10 0 10 20 30 40
rudder angle (deg)Number of rudder angles
Figure 22. Harmonie yaw with rudder action (b3) : distribution
of number and range of rudder angles.
no. o f transient cycles no. o f steady cycles waiting tim e
(min)
Figure 23. Harmonic tests (b): operational and analysis
parameters.
1 2 3 4Number of fwd speeds
0
1 2 3 4 5 6 7 8 No.of propeller rates
Figure 24.
1 3 5 7 9 11 13 15 Number of yaw rates
6 11 16 211No. of rudder angles
C/53
1 6 11 16 21Number of drift angles
c
te
5 10 15 20 25 30Waiting time (min)
Stationary circular tests (c): test parameters.
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X
-
Dynamics and kinematics o f ship model
Longitudinal force Lateral force Yawing moment Rolling moment
Propeller thrust/torque Rudder forces/moments Other forces/moments
Sinkage TrimRoll angle
Control parameters o f ship model
Rudder angle Propeller rpm Other
Control parameters o f mechanism : test type (a)
Carriage position/speed Drift angle Other
Control parameters o f mechanism : test type (b
Main carriage pos/speed Lateral position Heading angle Other
H
Control parameters o f mechanism : test type (c)
Arm position/speed Drift angle Other
0 20Number o f answers
40
I Always 1 Sometimes I Never
Figure 25. Data-acquisition: data measured during captive
manoeuvring tests
437
X