A
December 1976
MITSUBISHI TECHNICAL BULLETIN
No.116
.kim loop
MI
2. 1
.uivwOn the Unusual Phenomena
in Manoeuvring Motions of a Full Ship Model
of a Full Ship Model
TECHNISCHE IJNIVERSITEIT
Laboratorium voor Hiroshi Tagano*
Scheepshydromechanca Sh i geru Asa i * *
.Archief
Mekelweg 2, 2628 CD DeIft
TeL: 015 786873 Fax: 015 781838
On the base of the know/edge for the existence of two kinds of flow types at the stern of the self-propel/ed model of some high block coefficient ships, the so-called unusual phenomena in manoeuvring motions are examined by making the captive model tests at drifting angle and the turning tests on a fu/I tanker model. Since the tested model has mainly a f/ow type characterized by a high wake fraction, several kinds of stern fins were applied in order to obtain the other flow type.
From these experimental studies, it is concluded that the unusual phenomena in manoeuvring motions are closely related to the flow type at the stern of the model. The lateral force delivered at the stern in the flow type S is supposed to be thecause of the
unusual moment in turning motions, which mainly comes from the hull surface force due to pressure distribution around the stern.
1. Introduction
There is a common tendency for models of high block
coefficient ships that the directional stability decreases with
the increase of the stern fullness and the decrease of the ratio of length to beam L/B of a ship. However, it has
happened since early 1960s(1) that some fuller ship models showed the reverse tendency in contrast to the above, that
is, its directional stability became better. This was named
the unusual phenomena in manoeuvrability.
Usually it was thought that the unusual phenomena appeared only on a model and its full scale ship still fol-lowed to the above-mentioned common tendency. A typi-cal example of turning test results both for model and its ful scale ship is given in Fig. 1(2), where large differences
between model and ship are recognized at the range of
small t udder angle. Thus, discrepancy of directional
stabil-ity between model and ship has become one of the most important problems of some particular high block
coeffi-cient ships. Since then, various approaches have been made to solve the hydrodynamic mechanism of the unusual phe-nomena and to obtain a method to suppress them. (s) In a course of these studies, it was recognized that not only
the fluctuation of rate of turn but also that of propeller thrust, torque and revolutions were accompanied by the
occurrence of the unusual phenomena in turning motions.
On the other hand, the flow state around the stern of
a high block coefficient ship has been studied continuously
in Nagasaki Experimental Tank since 1960 with special attention to its contribution to the propulsive perform-ances.(6_(8) Through these studies it became clear that
some models with full stern had two kinds of flow patterns, i.e. types F and S and the value of wake fraction changed
according to its flow type. Fig. 2 shows a typical example of the difference of the flow types of a model measured in the same condition. In the figure, the flow types F (low
wake fraction) and S (high wake fraction) exist in the same
40
Port 30 -20 0 10 20 30 40 o(deg) u \/gLWL Fn = Model ShipFig. 2 Comparison of effective wake
Starboard
Dr. Engr., Resistance and Propulsion Research Laboratory, Nagasaki Technical Institute, Technical Headquarters
0.7
0.6
0.5
0.4
Fig. i Typical results of turning
O--- With fins ---,&-..- Without fins
A
tests
I
I I
test condition for the model.
Another important feature obtained by the above studies was discovery of the lateral force delivered at the stern of a model when the flow type became S. The
pre-sence of the lateral force reminds us of close relation of the
flow types with manoeuvring motions. lt must be stressed that the flow type at the stern can be changed artificially from S to F by use of stern fins and ¡t is also noticeable that the wake fraction of the same model with stern fins
coincides with that of the flow type F. We can realize both flow types of F and S as required, if we choose the model
and its test condition so as to be mainly the flow type S
without stern fins.
On the base of our knowledge summarized above, the
present study was planned for examination of the effect of
the flow types on manoeuvring motions and for the study of the hydrodynamic mechanism of the unusual
phenom-ena on manoeuvrability.
2. Model and its Test Condition
The model and its test condition are chosen so as to match the requirement stated in the previous section. Principal particulars of the ship model and the screw pro-pellers are tabulated in Table i and its body plan is shown in Fig. 3. This model is the parent one of the systematic series tests of SR 61 (Research Committee No. 61 of the
Shipbuilding Research Association of Japan).
The model has a normal rudder and the ratio of its area
to the lateral area of the model is 1/70 in 65% load condi-tion. In order to investigate the effect of direction of the propeller rotation, propellers with right and left handed rotation were adopted. Since the model has mainly the
flow type S under this test condition, several kinds of stern
fins were applied as explained later in order to obtain the flow type F.
Captive model tests at drifting angle were conducted in the Towing Tank with propeller running in 65% load
condition and at the speed of 1.188 m/sec (Froude number F= 0. 17).
Turning tests by use of the free running model were
conducted in the Seakeeping and Manoeuvring Test Basin at the same condition and speed.
L%IIIV
litai__
III
Ic!At'wIlIihNu51I
i Ui
LO 12W.. 1OWL 6WL 4WL 2W1.. IWL BL 8WLFig. 3 Body plan of tested model
Table 1 Principal particulars
Gond. Full load 65% load
5 000.0 5 000.0 B 833.3 833.3 dM 301.9 202.3 Trim 0 50.OA
L/B
6.000 6.000 B/dM 2.760 4.120 Cb 0.8019 0.7781 C, 0.809] 0.7894 Cm 0.9904 0.9857 AR/LPP.dM 1/104.5 1/70.0 Prop. RH LH D 141.8 141.8 P 0.8403 0.8403 Ae/Ad 0.4912 0.4912 d/D 0.1806 0.1806 Z 5 5Direction Right handed Left handed
of rotation
(Unit in mm
Water surface
Without fins
Fig. 4 Schematic flow pattern around stern
3. Preliminary Experiments
3.1 Stern Flow Observation
To clarify the effect of the flow type on manoeuvring motions it was necessary to investigate the state of stern
flow by some means. For this purpose a submergible movie camera was used to visualize the stern flow. As a result, it
was found that, near water surface before the propeller,
downward streams are observed and some-times air bubbles are drawn toward the propeller. The schematic flow pattern ¡s illustrated in Fig. 4. From the analysis of propeller thrust and torque measured at the same time, the flow pattern at this moment was found to be type S.
3.2 Control of the Flow Type by Stern Fins
The above-mentioned facts provided an idea that if downward streams were prevented near water surface
before the propeller, the flow pattern would change from type S to the other. To prevent downward stream a pair
of stern fins was chosen as a flow regulator. Arrangements of five kinds of the stern fins devised by this idea and used in the tests are shown in Fig. 5. Specific features of the fins are as follows:
FIN-1: Original fins designed from the results of flow
visualization in the preliminary tests.
FIN-2: Fins with the same shape as FIN-1 and shifted
rearward from FIN-1.
FIN-3: Fins expanded 1.5 times wider in breadth than
FIN-2.
FIN-4: Fins doubled in breadth from FIN-2.
FIN-5: Fins expanded rearward in length and widely in
breadth from FIN-4.
Typical results of stern flow regulation are shown in
Sec-tion 4.3. AP No.2 No.3 No.4 No.5 No.1
Fig. 5 Arrangement of stern fins 4. Effect of the Flow Type on Turning Moment
4.1 Procedure and Items of Measurement
A schematic explanation of the captive model tests at drifting angle is shown in Fig. 6. That is, the ship model with propeller running was captured at the angle of inclined from the towing direction by a fore and an aft
guides. Items of the measurement were lateral forces F (at
the fore guide) and A (at the aft guide), rudder normal
force FN and propeller thrust and torque. From Yp, YA and FN obtained in the tests, turning momentN of the hull and turning moment NR due to rudder force FN were
calculated.
N, N e
VF
N=YF-EFYA LAFN LA
NR =FN L n
a : Propeier beariog force
Fig. 6 Captive model test at drifting angle with propeller running
4.2 Effect of Direction of the Propeller Rotation The model with the flow type S is accompanied with
lateral force at the stern even on a straight course as
men-tioned previously. The direction of this lateral force seems to be determined by the direction of propeller rotation. To investigate the effect of direction of the propeller rotation,
experiments were carried out by use of propeller with both
right and left handed rotation. Turning moment N and NR were obtained in each case of "without propeller", "with RH (right handed rotation) propeller" and "with LH (left
handed rcrtation) propeller".
Fig. 7 shows the variation of N and NR with respect to i3 and it is found that there is a discontinuity of N in the case of "with propeller", while no discontinuity is found in the case of "without propeller". That is, N in the case of RH propeller changes discontinuously at ß = 1.5 deg and N in the case of LH propeller does at ß = 1.5 deg. These
1/2 1/4
0.5 L,. ®._e_._e_ O.. 2 NR (kg-m) ---Without propeller -O----.Mth LH propeller Wìth RH propeller
Fig. 7 Captive model test results (1)
changes of N amount to about 1.3kgm in turning moment and are equivalent to 9.3 deg in rudder angle 6 from the relation of N and 6 (N= 0.1406 where N in kgm andö in degree) obtained from the rudder performance test in behind condition. lt can be said that this amount of rudder
angle is considerably large even if we take the small rudder
area ratio of the model into account. lt must be noticed
that discontinuous changes are found at the certain i3 when the flow pattern is type S, in the case of this tested model. The turning moment IVR changes also at the same /3 in the
case of "with propeller", however, the amount of change
of NR is much smaller than that of N.
Differences of N between "with propeller" and "without propeller" are shown in Fig. 8. From this figure, RH
propeller generates left turning moment and LH propeller
does right one on a straight course (/3 = O deg) as the effect of the lateral force at the stern. This fact leads us to an idea
that the lateral force due to the flow type S will exert also
a considerable influence on manoeuvring motions.
43 Effect of the Stern Fins
In order to investigate the effect of the flow type on
turning moment, captive model tests at drifting angle were conducted and it was examined how the five different stern
fins worked in turning moment. Fig. 9 shows the
experi-mental results of FIN-1 and 2. The position of the stern fins
is one of important factors for flow regulation because
6
4 6
FIN-2 shows much stronger effect than FIN-1. The effect of the breadth of the stern fins on turning moment is also shown in Fig. 10, in which the widest stern fins FIN-4 almost smooth the discontinuity of N which is occurred
at 3 = 1.5 deg for the other kinds of fins.
In the case of "with FIN-4", the observed results by the submergible camera revealed that the downward stream
toward the propeller almost disappeared, except that some-times a few air bubbles were still drawn around the trailing edges of the stern fins. Thus FIN-5 was devised by expand-ing the length of FIN-4 rearward until ¡t reaches the rudder.
Fig. 8. Turning moment induced by propeller rotation
o //
/
71
II
zN (kg-m) 1.0 0.5 N (kg.m) 2.0 o 1.0 With LH propeller =0. - Without fins--O-- With FIN-1
-'- With FIN-2
/
Fig. 9 Captive model test results (2)
¡9 (deg) 6 ß (deg) o 0.5
_o.--___
"-I 2.06
4
2
0--
- 1.0 RH propeller o LH propeller6 With LH propeller Without fina With FIN-2
---
With FIN-3---'
With FIN 4Fig. lo Captive model test results (3)
Effect of FIN-5 is shown in Fig. 11. It is confirmed that FIN-5 has the most marked effect among all stern fins tested and a schematic flow pattern in the case of "with
FIN-5" is illustrated in Fig. 12.
5. Experiments for Components of Turning Moment Generally speaking the lateral force delivered at the stern
may come from the following three causes. The first is
Fig. 12 Schematic flow pattern around stern (with FIN-5)
/7
/V/
With LH propeller = o. Without tins ---V-- With FIN-4 Wth FlN-5Fig. 11 Captive model test results (4)
rudder force, the second is force due to hull surface
pres-sure and the last is propeller bearing force. In the previous
section, it was shown that rudder force is not a main part
of the lateral force delivered at the stern in the case of i5 = O
deg. In order to clarify the contribution of the other two components, hull surface pressure around the stern and
propeller bearing force were measured in the captive model
tests at drifting angle with propeller running and without
propeller.
The results of pressure distribution obtained in the tests
are shown in Figs. 13-17. Fig. 13 shows the pressure dis-tribution for the captive model on a straight course (ß = O deg) without propeller. In the case of "without propeller",
the pressure distribution is almost the same on both sides of
the model. Figs. 14 and 15 show the pressure distribution in the case of "with propeller" and on a straight course,
for port and starboard sides respectively. Considerable dis-crepancies are found in these figures of the pressure
distri-butions. Difference of the pressure distributions is shown in Fig. 16, where the differences are distinctive around
the positions indicated by black dots. Mean values of
pres-sure differences at the points are plotted with respect to ß in Fig. 17. It can be said from Fig. 17 that the change of
ß (deg)
7M.,
A
T
Fig. 13 Pressure distribution on hull surface (without propeller, 3 = O deg)
"t
6WL
3
BL
Fig. 14 Pressure distribution on port side hull surface (with LH propeller, ß = O deg)
Fig. 15 Pressure distribution on starboard side hull surface (with LH propeller, = O deg)
P P : Pressure Cp= Density of water p U U Model apead S.S. AP 1/4 38 1/2 5,8 S.S. AP 14 3./8 1/2 5/8 S.S. AP 1/4 3/8 1/2 5 '8
-6
4
2
Fig. 17 Difference of pressure distribution
port
pressure difference corresponds qualitatively to the results
of turning moment obtained from the captive model tests
shown in Figs. 7 and 8. Integration of the pressure distribu-tion around the stern gives also a good correspondence to the lateral force delivered at the stern quantitatively.
On the other hand, propeller bearing force was also measured in the captive model tests at drifting angle and the results showed that it is very small compared with the lateral force delivered at the stern and that the variation with respect to ß does not correspond to turning moment
curves shown in Fig. 7.
From these results, it may be concluded that the lateral force which characterizes the presence of the flow type S is
PpPs
ACp= Ps : Pressure on starbord
- Pp : Pressure ori port
--®--- Without propeller
-O- With LH propeller With RH propeller
Fig. 16 Difference of pressure distribution between on port and starboard side
mainly due to the difference of hull surface pressure on
both sides around the stern and that the contribution of the
lateral force due to the rudder force or the propeller bear-ing force is small enough in comparison with the hull
surface force.
6. Effect of the Flow Type on Turning Motions
In the previous sections, it was clarified that the flow ß (deg) type affects the turning moment of the captive model at drifting angle. In this section it is shown that how the flow type affects turning motions. For this purpose the turning
0.8
0.6
6WL
4
Fig. 18 Turning test results (1)
starboard 20 30 ö (deg)
0 i
0 0.2 --0.4 Without fine --0.6 -- With RH propeller----A--- Wth LII propeller
--0.8
S.S. AP 1/4 3/8 2 5/8
0.4
tests by use of the free-running model were conducted
especially for the range of small rudder angle.
6.1 Effect of Direction of the Propeller Rotation The turning tests were conducted by use of the free-running models with RH and LH propeller and with rudder angle S = 20 to +20 deg and the results are shown in Fig. 18, where unusually stable zones are clearly noticed. Fig. 19 is an example of the records, which shows that about 4 deg check helms are executed to hold a course straight
and after rudder angle is kept at midship the model starts to turn right and left corresponding to LH and RH
propel-ler respectively. The direction of the check helms and
that of turning motions are all consistent with the direc-tion of turning moment obtained in the captive model tests at drifting angle. For example, the heading angle in the case of "with LH propeller" begins to decrease at about 15 seconds after rudder angle is kept at midship
and begins to increase again. This behaviour is thought to be caused by shift of the lateral force at the stern from the starboard side to the port one. In fact it was observed that
the disturbance of water surface around the stern moved
also from one side to the other during the turning tests.
6.2 Effect of the Stern Fins
Among five sorts of the stern fins described before,
o
Time (sec)
Fig. 20 Example of records (2)
Without fins
With LH propeller With RH propeller
Fig. 19 Example of records (1)
O
FIN-2, 4 and 5 were used for the turning tests. Fig. 20
shows an example of the records (5 = O deg) in the cases
of "with FIN-2" and "without fins". During a straight
course run, check helms are about O deg and about 4 deg
for "with FIN-2" and "without fins" respectively. After rudder angle is kept at midship, the model runs on almost straight course for "with FIN-2", whereas it turns to right
for "without fins".
Both behaviours during a straightcourse run and after the rudder is kept at midship provide
a clear evidence of the stern fins' effect. Fig. 21 shows the
effect of the stern fins in the turning tests of 8
20 to
+20 deg and it also shows that the unusually stable zone is
made narrower (5 = 4 to +4) by the stern fins than the original one (5 8 to +8 deg) of "without fins". Among five different stern fins, FIN-5 is the most effective for suppressing the unusual phenomena. That is, the better the smoothing effect of the discontinuity in turning mo-ment is, the larger the influence of the stern fins on the
unusual phenomenon is. In other words, the lateral force delivered at the stern of the tested model in the flow type
S seems to cause an unusual moment which prevents
turn-ing motions, so that it induces unusual increase of the
course stability. 15 30 Time(sec) "3 0) D 0O O be 't QQ D O D 'QQ be O D -s
5
4-2 f.. ii- -/
15 'Jt'i.i\jl.íVJ'j ', t. 15 Time(sec) With LH propeller Without fins ---With FIN-2 30 5-a, Q) QQ (t O D o O o o 15 30 Time(sec) O bQ be D D = S{
port
10
0.8
0.6
Fig. 21 Turning test results (2)
7. Analysis of Unusual Moment by Simulation of Turning
Motions
In the preceding section, it was found that the lateral force delivered at the stern in the flow type S worked as an unusual moment in turning motions and the unusual moment was estimated by the results of captive model
tests at drifting angle. However, since the evaluation of the
unusual moment was all made at the steady condition, a following question arised: "Does the unusual moment cause quantitatively unusual motions under the unsteady condition?". To answer this question, the simulation of
manoeuvring motions was carried out by use of the charac-teristics of the unusual moment.
Denoting that the unusual lateral force and the unusual
turning moment by and respectively, the
equa-tions of moequa-tions including 3rd order nonlinear terms can
be written as follows:
(mo+mx)UYr
V V r Nr r IY,.jYv,.Yrr V2 vr INvvNvrNrr r2 t'vvv YvvrYvrrYrrr v2r vr2 NvvrNvrrNrrr r3 starboardm0+m Y m,ct
N
fYYg
fYun-
(1) Fig. 22 Hypothetical model of unusual moment30
20
/
V II/
ja' I/ Áac®
7/-O - 0.2 0.4 0.6 0.8 10 20 30 4 (deg)o Without tiria
--a--With FIN-2 ---V--- With FIN-4 ---®---- With FIN-5where
m0+m. mycty
coefficients of inertia termsof swaying motion
coefficients of inertia terms
of yawing motion
Y,
(mo+mx)UYr
coefficients of linear damp-ing terms of swaydamp-ing motionNy,Nr coefficients of linear
damp-ing terms of yawdamp-ing motion
V' "vr, 'rr' Y VV' coefficients of nonlinear
'vvr, 'vrr' 'rrr damping terms of swaying
motion
N v Nvr, Nrr, N coefficients of nonlinear
Nvr, "'Vrr' Nrrr damping terms of yawing
motion
Y6, coefficients of lateral force
due to rudder execution
N,Ng
coefficients of yawingmo-ment due to rudder execu-tion.
From the results obtained, specific features of the
un-usual moment can be summarized by the following items:
Lateral force at the stern works as the unusual
moment.
Rudder normal force changes also when the unusual
moment appears.
Turning moment in the case of "LH propeller" for
example has the discontinuity at j3 = 1 .5 deg.
Regarding (A) and (B), we can replace furz and by
Besides, the observed results of the turning tests suggest that shift of the lateral force at the stern requires some delay. Then it is more natural for the equivalent rudder
execution due to the unusual moment to have some rate of
steerage.
From the foregoing considerations we can assume hypothetical external force moment and equiva-lent rudder angle which are graphically shown in Fig. 22. The unusual moment in Fig. 22, for example, has
such a peculiarity that falls down at i = on a way of increasing i3 and goes up at ß = í2 on a way of decreasing 3. In other words, they have the hysteresis characteristics as
described in Fig. 22 where the shifting speed from or
ß2 is prescribed by the rate of equivalent rudder angle 5.
Eliminating of sway terms in Eq. (1) as nonlinearity of swaying motion has little effect on yawing motion, then
Eq. (2) is obtained as follows:
T1T2 +
(T1+T2)i+r+a2r2+cu3r3
(2) 6 4 2 o o o 0.5 o 4 2 02
-4 1.0 0.5---2 'u4
a) -o6
'0 S. -/ / //
-I/
/ / / / S./
/ S.,/
S.,Fig. 23 Comparison of turning test records and simulation
,/
S,,/
'\
//
'S/
'Q/
n Experiment Simulation 30 Time (secwhere Therefore is expressed in the form of Eq. (4).
T1T2 = K P4/P31 (4) T1T2= P2/P31 KT3 ='P5/P31 a2 =P32/P31 KT42 =P6/P31 a3 = P33/P31 =P7/P31 T1 = (p2+'S%/p-4PIP31)I2P3I T2 =
(P2\'P--P1P31 )/2P31
Pi =-
(ma)(ma)
P2 =-m7a7 (mo+mx)U_Yr}_ (m0+m)N,.
+m7ciN- (i+J) Y
=N,, (mo+m) UYr
+ YvNr+ 2 myayY,r- (rno+my)N,r}
P32 =
YvNrrNv Yrr+3myay Yrrr
- (m0+m) Nrrr
=YvNrrr N
rrrP4 =NY5
-PS =(m0+m)N5 - rna Y5
+N Y - YVN
P6 =(m0+m)N - rna Y
P7 =N
-
(3) 'S 'S S. 'S 'S 'S. _t 'S 'S.
S. 20 10The manoeuvring derivatives in Eq. (4) are obtained by the
captive model tests at drifting angle and by the rudder angle tests. Then the value of is evaluated about 5.0
deg. A practical approximation can be applied with
substi-tution of
into the first order approximate equation.lt yields the following expression:
T,+r=K(6 +6un)
(5)where 6, has the property shown in Fig. 22.
As an example of the simulation of turning motions,
the turning test of 6 = 2 deg is chosen, because its records
show typical yawing motion which is characterized as the occurrence of the unusual phenomena. Four parameters
of
6,
i and ß2 are determined by analyzing therate of turn obtained by turning tests. An example of the simulation results is shown in Fig. 23 where experimental
ones are also compared, while the behaviour of 6 used in
the computation is shown in Fig. 24. As a whole the
com-puted results are in good agreement with the experimental
ones except the first peak of the rate of turn. In spite of the simple formulation of Eq. (5) and the simple charac-teristics of as shown ¡n Fig. 24, the computed yawing
angle and the rate of turn in Fig. 23 simulate a periodic change of the rate of turn fairly which is a typical charac-teristic of the unusual phenomena. This fact may support the validity of such simplification for the unusual phenom-ena as a first step, although they come from the
compli-cated viscous effect of the stern flow.
As a result of the simulation of turning motions, it ¡s
inferred that the amount of the unusual moment derived from the captive model tests at drifting angle can almost coincide with the amount for the occurrence of unusual
course stability of the same model.
8. Conclusion
Stdrting from the basic knowledge about the stern flow types of full ship forms, the authors examined the cause of the unusual phenomena ¡n manoeuvring motions ex-perimentally. The results of the study can be summarized
as follows:
The authors wish to express their deep appreciation to
Dr. K. Watanabe, vice-manager of Nagasaki Technical
Institute, Dr. H. Fujii, manager of Seakeeping Research Laboratory and K. Tamura, manager of Resistance and
Propulsion Research Laboratory, for their continuing
Acknowledgement 025 8un (deg) 4
4
Fig. 24 Characteristics ofLateral force delivered at the stern of the tested model in the flow type S is the cause of the unusual moment in turning motions.
Lateral force comes mainly from the hull surface
force due to the pressure distribution around the stern. Hull surface force is induced by the propeller rotation.
Stern fins are effective to control the flow type and they work also as an effective suppressor against the
so-called unusual phenomena.
By using the results of the captive model tests at
drift-ing angle and of the computation of turndrift-ing motions, a hypothetical but practical simulation model of the
unusual moment ¡s provided.
Although the unusual phenomena were first recognized
in manoeuvring model tests, it was reported that the similar phenomena might appear recently at some full scale ships too. Considering the fact that the present
results are derived from only one ship model, further
in-vestigation will be necessary to obtain the generalized conclusion. But the results of this experimental approach will be effective and become of some help to the studies
on the phenomena of the full scale ships.
guidance and encouragement. The authors also wish to
express their appreciation to the members of the Nagasaki
Experimental Tank of Mitsubishi Heavy Industries Ltd.,
for their cooperation in carrying out this investigation.
0 1.25
Nomoto, K.: Unusual Scale Effect on Manoeuvrabilities of Ships with Blunt Bodies, Proceedings of 11th ITTC (1966)
Fujil, H.: Law of Similarity for Manoeuvrability of Ships,
Mitsubishi Juko Giho, Vol.4, No.2(1967)
Motora, S. et al.: An Analysis of the Manoeuvrability of a
Ship Associated with Unusual Characteristics under Steerage, J.
of the Society of Naval Architects of Japan, Vol.128 (1970) Okamoto, H. et al.: Correlation Studies of Manoeuvrability of
Full Ships, J. of the Society of Naval Architects of Japan, Vol.
131 (1972)
Sato, S. et al.: On a Study of Ship-Controllability of a
Wide-References
Beam Tanker, J. of the Society of Naval Architects of Japan, Vol.134 (1973)
(6) Watanabe, K.: Unstable Phenomena of a Full Ship, Mitsubishi Juko Giho, Vol.4, No.4 (1967)
(3) Taniguchi, K.: Problems Connected with Model Tests for
Large Merchant Ships, Introductory Statement in Group
Dis-cussion, Proceedings of 12th ITTC (1969)
(8) Watanabe, K.: Unstable Phenomena in the Self-Propulsion
Tests of Full Ship Form Models, J. of the Society of Naval
