PAPERS
OF
SHIP RESEARCH INSTITUTE
A Consideration on the Extraordinary Response of the Automatic
Steering System for Ship Model in Quartering Seas
By
Takeshi FUWA
November 1976
Ship Research Institute
Tokyo, Japan
2
ARCHIE
Technische Hogesckooi
Deift
[!4Papers of Ship Research Intitute,, No.. 50 (November 1976)
A CONSIDERATION ON TEE EXTRAORDiNARY
RESPONSE OF THE AUTOMATIC STEERING SYSTEM
FOR SHIP MODEL IN QUARTERING SEAS*
By
Takeshi FUWA**
ABSTRACT
In the Seakeeping Model Basin of the Ship Research Institute, an ãüto matic steering system for ship model is uSed to keep its course in waves.
Basically this system is a continuous PD control for the heading angle devia tion and it was experimentally designed to have satisfactory response charac
teristics both in calm water and in waves
Occasionally unexpected longperiod response of the steering system was observed in the quarteringor fol
lowing sea condition. This response is not preferable to perform more
ac-curate measurement It is also Important practically because similar response
of an actual ocean going ship has been reported.
In the present paper the mechanism of the response has been investigated
By the results of analogue computer simulatiOn, the cause of the response
has become evident. . Because of the non-linear elements of the system, i.e.
sãtüratiofl in steering velocity and rudder angle limitation, the response whOse period is longer than encounter period is possible to be excited bywaves To
prevent the unpreferable response some comments and specifications for the automatic steering ysteth of the ship model are shown.
* Received on Jul' 13, 1976.
** Ship Propulsion Division
CONTENTS
Abstract
Nomenclature
Introduction
Experiment in the Seakeeping MOdel Basin Analogue Computer Simulation
Comparison of Results between Tank Test and Simulation
5 Comments on the Automatic Steering System in the Seakeeping
Model Basin 6. Conclusion
Model
(=r.)
Rudder Angle of Ship Model Directed Rudder Angle Heading Angle of Ship Model
Initial Heading Angle of Ship
Model
Directed Course Angle
Course Angle in the Experiment Circular Frequency
Encounter Circular Frequency
of Ship Model with Waves Velocity of Ship Model Velocity of Ship Model in Calm
Water (5=00)
Radius of Turning of Ship Model
Length of Ship Model Wave Length
Wave Height
1.
INTRODUcTION
After disasters of gigantic ore-carriers in the
Pacific Ocean, a
re-search project on the safety of gigantic ore-carriers
had started in the
Ship Research Institute
The objective of the project was to establish
the method of estimation of wave loads precisely in various sea
condi-tions, and to offer useful data to ship hull
designers.
By using a free running ship model,
systematic experiments in
re-gular or irrere-gular waves were performed in
the Seakeeping Model
Basin of the Ship Research Institute
Hydrodynamic pressure,
impul-sive water pressure on the hull, relative wave height shipping water,
ship motions and ship performance in waves were measured in various
conditions I
An automatic steering system was designed and used to
keep the course angle of the ship model in waves.
By means of this
steering system, average heading angle of the model was kept constant.
Occasionally, however, yawing oscillation, whose
period was
unexpected-ly longer than encounter
period, was observed.
This long period
re-sponse was remarkable
especially in the following or quartering sea
condition
This response is not preferable to perform more
accurate
measurement, and moreover similar response of an
actual ocean-going
ship was reported."
To examine the mechanism and cause of the response, model test
was conducted in the quartering sea
condition for several combinations
of parameters of the automatic Steering system.
Analogue computer
simulation for the system was also performed.6
K: Gain Constant of Ship Model
T Time Constant of Ship Model
Time COnstant of Steering De- S
vice 5*
Feedback Gain for Proportional 8 Control
Feedback Gain for Rate Control Time Constant of Low Pass
Fil-ter x
5m00 Maximum Rudder Angle U
Maximum Steering Velocity we
a1, a2: Constants of Feedback System
fc CutOff Frequency of Low Pass U
Filter U0
Yaw Rate of Ship Model
r
Yaw Rate of Ship Model due to RSteering L
Yaw Rate of Ship Model excited 2
by Waves H
Fig. 1. Body Plan of Ship Model
3
2
EXPERIMENT IN THE SEAKEEPING MODEL BASIN
Course keeping tests in waves were carried, out in the
Seakeeping
Model Basin
(80 m x 80 m x 4 5 m) of the Ship Research Institute by
using 4 5 m model of ore-carrier "Kasagisan Maru" which
is one of
the standard ship models for seakeeping test
in Japan
In Table 1
principal particulars of the ship model
are shown
Body plan of the
model and the Seakeeping Model Basin
are shown in Fig 1 and Fig 2
respectively.
The automatic steering system is continuous feedback control for
the heading angle deviation from the
course
Feedback gains of the
proportional control k1 and the rate control k2 can be changed
Toavoid useless steering of high frequency and large angle of
rudder
a low pass filter and a limiter for rudder angle are added
According
to the test condition, cut-off frequency of the filter f,, and the
maxi-mum rudder angle ô
can be chosen.
Table 1. Principal Particuiars of Ship Modei Length between perpendiculars 4.5000 m
Breadth mid. O.7397rn
Depth mid. 0.4190m
Draft mid. 02915rn
Dispiacement 0.8013 t
Block coefficient 0 8243
Midship coefficient 0.9975
C.G. from idship fore 0.1330m
C.G. from keel 0.239 m
Metaeentiic radius 0.069 rn Longitudinal gyradius 0.238L
Transverse gadius
0.360 B1Rolling period 2.01 sec
Rudder area 0.0196 rn2
Rudder area ratio 0.0149
Bilge keel breadth 0.0077 m
Bilge keel length 1.1353m
NO.1 WAVE MAKER(..FLAP)
II
WAVES PORT) BEACH SEAKEEPINGMODEL BASI N (8OmxBQmx4.5m)Fig. 2. The Seakeeping Model Basin
Table .2. Test ConditiOns and Measured Results
±
C.)
w
F.P.=FuII Pass Filter, X=45° (Quartering Sea), 2/L=1.25,
H=L/50,
Regular Wave, U=L03m/s System Period (sec) Heading (deg) Yaw Rate (deg/sec) Ruddle Angle (see)k1', k2' long short long short long short long short
1 2,1 0.3 ±35 2.45 - L67 5.04 15.46 2 ±15 2.17 - 1.71 5.10 14.12 3 ± 5. 2.40 2.17 5-21 5.00 4 3,1 0.3 ±35 2.45 167 5.02 15.53 5 3,2 0.3 ±35 7.20 2.44 1.25 1.83 0.55 485 24.0 14.10 6 0.5 12.00 2.40 0.59 1.92 no data 4.24 14.12 7 1.0 13.40 243 1.17 1.84 0.37 4.85 5.29 15.53.
8
F.P. 14.80 2.40 0.88 1.25 0.18 5.02 4.24 15.53 9 0.3 ±15 2.44 . 1.67 4.77 14.40 10 5,3 0.3 ±35 9.33 2.40 2.90 1.67 1.09 4.85 31.77 10.59 11 0.5 10.90 2.40 2.92 1.70 0.92 4.76 14.12 24.71 12 1.0 9.08 2.41 4.48 1.70 101 4.76 24.7.1 15.53 13 F.P. 1400 2.39 2.33 1.70 0.63 4.76 16.24 1483 14 0.3. ±40 8.55 2.36 2.92 1.92 0.96 4.67 43.07 12.71 15 ±30 2.44 1.83 5.12 14.83 16 ±25 2.48 1.83 4.94 13.99 17 ±10 2.46 1.75 4.92 8.97IVAW PATE O HEADITG ENGLE 6 RUDDER ANGLE AW RATE lOsec S HEADING ANGLE 6 RUDDER ANGLE
Fig. 3(a). Response Pattern of Tank
Test
(k1, k2), ömox,fc(5,3), 35° F.P.
Fig. 3(c). Response Pattern of Tank Test (k1, k2), Ômox,fc=(3, 2), 350, F.P. N, 'I, 0rTI r'YAW RATE S HEADING ANGLE
Fig. 3(d). Response Pattern of Tank
Test
(k1, Ic2), 5moo,fc=(3, 2), 350 0.3 Hz
5
Experiment was carried out to keep the course angle of the ship
model constant in waves by means of the automatic steering system
Heading angle, yaw rate, rudder angle, ship position and ship speed
were measured
The experiment was performed in the quartering
re-gular waves.; X=45°, A/L=1.25, H=L/5O
In Table 2, test conditions
and measured periods and amplitudes of heading angle, yaw rate and
rudder angle are shown.
The short period of the response corresponds
with encounter period of the ship model with waves.
Typical patterns
of the response are shown in Fig. 3, in which parameters of
experi-ment are feedback gains k1 and k2, limitation for the maximum rudder
angle
and cut off frequency of the low pass filter f.
Responses,
whose periods are longer than encounter period, are observed in these
patterns
Characteristic feature of the response is triangular or
trape-zoidãi shaped response pattern in rudder angle.
From Table 2 and Fig. 3, effect
of each parameter on the
re-sponse can be seen as follows.
As the cut-off frequency of the low
pass filter f,, becomes smaller, the period of longer response becomes
ti
Id r VA' RATE II) secV
ADI N ANGLE[\A f
/ \JL/' V V V
6 RUGER AA3LEFig. 3(b). Response Pattern of Tank
Test
shorter.
The larger the gain constant of the proportional cOntrol k1
or the smaller that of the rate control k2, the less stable the system
is
When the maximum rudder angle
ômflXis small, the response of
longer period is suppressed
There are three or four kinds of response
patterns as shown in Fig. 3..
To know manoeuvering characteristic of the ship model, spiral test
and sinusoidal steering test were performed in calm water
A course
change test with the automatic steering system was also performed
and closed kop step response of the total system was measured.
In
SPIRAL TEST
ksogidn
rrrclru (4 5fl) 400- -20
, Q0 2 SINUSOIDAL STEERING TEST r (0/ 4.0 rod/sec 1.0Fig. 5. Spiral Test Result
U0
0
I Table Characteristics of the System K =0.15231/sec T=33sèc
Tg =O.S7i4secmx292 deg/sec
a1 =2.66 a2 =0.25sec k1 =a1 k2 =azk2' T =1/2rfc Fig. 4. Spiral Test ResultFig. 4 and Fig. 5, the results of spiral test and sinusoidal steering
test are shown respectively
From these results it is found that
non-linearity of manoeuvering characteristic of the ship model is not so
large, considering speed down due to the ship motions and using
non-dimensional angular velocity r'
Therefore,
it
is assumed that the
manoeuvering characteristic of the model can be represented by a linear
system in first order as shown in Table 4, and that it is unchanged
even in waves.
Values of manoeuverability indices K and T
deter-mined by the tank test are shown in Table 3 with other
charactefis-tics of steering devices and automatic steering system
The results of
the a.itomatic. course change. test in calm water show that the
re-sponse of yawing has damped quickly under any condition shown in
table 2, and that nature of the response has been able to. be explained
qualitatively as nature of linear system except partial saturation in
the rudder angle;
3. MALOGUE COMPUTER SIMULATION
With an analogue computer, simulations of the response for the
course keeping test and course changing test both in waves and calm
water have been performed.
Equation of motion and other relations are. shown in Table 4, and
block diagram in Fig; 6;,
Upper limit of revolutions per second of the steering thotor
intro-duces saturation in steering velocity.
Cause of the triangular or
trape-zoidal pattern of rudder angle response is thought to be saturation in
angular velocity of rudder angle due to the steering velocity limitation
Table 4. Equation of Motion and Other RelationsManoeui?ing Characteristic of
Model Ship
Ditected Rudder Angle
Steering Vëlbcity
Limit of Rudder Angle
Characteristic of Steeriiig Device
Angular Velocity of Yawing
Heading Angle of Model Ship
T.-±r=Kö
(1)
_o*=ki.(e_oi*)+k2.r* (2)
do"(3)
()
Ômx,(5)
r*_r+r
(6)
G=oo+5r*.dt(7)
y
>-I
LL>
AUTO PILOT L LOW PASS FILTER
6
-> o
6STEERING 9/STEM STRSPD QJ& RJDJER ANG.
Fig. 6.. Block Diagram of the System for Simulation
In the simulation of course keeping or course change in waves,
steer-ing velocity is set constant for convenience of' programmsteer-ing and
com-parison with analytical method
In the block diagram there are two
non-linear elements representing the saturation in the steering velocity
and the limitation of rudder angle.
Inputs to the system are angle of
course change e0 and excitation in yaw rate by waves r.
From the results of simUlations the followings are known.
Concerning with course change with the automatic steering
system in ëalm water, responses of the system can be explained' as
those of linear system.
When the feedback gains are large, steering velocity and
rudder angle are apt to saturate in case of large angle of course
change and therefore non-linear effects appear in the response.
De-creasing the steering velocity to a certain limit in calm water
condi-tion, stable linear system diverges with the non-linear effects of
steer-ing velocity.
In this case limitation of rudder angle suppresses the
divergency.
Combining the triangular response pattern owing to course
change with the response excited by waves, similar patterns as those
of tank test results have been obtained.
Without the non-linear
ele-ments, however, the longer period response converges rapidly and its
period is shorter than that of the tank test result.
Increasing the amplitude of excitation by waves r, non-linear
system which is stable in calm water diverges or shows a limit cycle
response.
When the limit cycle response progresses well, the response
of encounter period is completely suppressed by the longer period
re-sponse.
Then the response of rudder angle shows trapezoidal pattern,
i.e. steering has become a kind of Bang-Bang control.
The larger the
amplitude Of exciting term of wave, the longer the period of the
re-sponse
Examples of response patterns obtained by analogue computer
simulation are shown in Figs.
'and 8.
d
t -___-
i--:-Fig. 7(a). Response for Course Change
in Waves (Simulation) (kj, k2), Ômx, f=(3, 2), 0.5 rad, 0.3 Hz, r=0.128 rad/sec
L
I II 1 1 -,:i L_LI
IIIi:pJiJ_
._°r7Lii
rI
T-ET T/-:[i .:T:
I-I--a- H ,-4-I --L -I-1-,/-!
ii±Litf
:1:1- 1-___I_1__
r_
Fig. 8(a). Response for Course Change
in Calm Water (Simulation)
(k1, k2), öm,fc(5, 3), 0.5rad, F.P.,
00=0.25rad, r=0
----!
_t I
Fig. 7(b). Response for Course Change
in Waves (Simulation) (k1, k2), 0mx, f0=(3, 2), 0.5 rad, 0.5 Hz, rw=O.l7 rad/sec
H1L}J1'fti- ±
o-IrI-i
Iii
IiiVL
Lj 1i
1Osecj ---i-F ---i-F rr O.OB5 r1d/sec _l LtI. - -- ---
-j-I--j-- _:_. - -II T
Fig. 8(b). Response for Course Keep-ing in Waves (Simulation) (ki, k2), ômx, f=(5, 3), 0.5 rad, F.P.,
Oo=0, r,,=0.085 rad/sec
9
may be suppressed by periodic external input.
This is called
"quench-ing phenomenon ".
Assuming the longer period response to be natural
oscillation of the whole steering system, quenching phenomenon can
not be recognized at all.
On the contrary existence of the exciting
term of waves reduces stability of the natural oscillation.
(6)
Parametric excitation by wave, which is caused by
depend-ence of exciting term on the heading angle of ship,9 does not come up
until wave height becomes ten times larger than that of the tank
ex-periment when other parameters are fixed.
4. COMPARISON OF RESULTS BETWEEN TANK TEST
AND SIMULATION
Comparing results of tank test with those of simulation, following
reasoning is possible.
The longer period response observed in the tank
test can be considered as a natural oscillation of the steering system.
Because the period is not necessarily integer times of encounter period,
it is said that the response is not subharmonic oscillation of wave
ex-citation
Qualitatively speaking, effects of parameters of the steering
system on the property of the natural oscillation obtained in the tank
test are explained even if the system is regarded as a linear system.
But it is impossible for a stable linear system to have a limit cycle,
and all the systems of tank test except for the case in which
para-meters are represented as (5, 3), 0.3, are linearly stable.
Consequently
non-linear model of the system is necessary to explain the existence
of limit cycle.
Considering the results of simulation, the cause of divergence is
saturation in steering velocity.
Limitation of maximum rudder angle
lets the response of the system into a limit cycle.
Because non-linear
property of the ship model shown in Fig. 2 (rö curve) suppresses
the progress of the response into the limit cycle, transient condition
of the response is kept for rather a long time. In view of yaw rate,
non-linear property of the ship plays just a same role as the
limita-tion of rudder angle, i.e. either property suppresses to produce large
yaw rate for large directed rudder angle.
Quartering or following sea condition is not essential in itself for
the. existence of the longer period response.
Qualitatively speaking,
however, in these sea conditions encounter period of the ship model
with waves become longer and it comes nearer to the period of the
natural oscillation of the steering system.
Moreover angles of course
change in these sea conditiOns were large because of experimental
con-dition in the Seakeeping Model Basin.
These may be the reasons why
the extraordinary long period response were remarkably observed in
following or quartering sea condition in the tank experiment.
The response pattern in Fig. 3 (a) can be regarded as a sustained
oscillation of triangular shaped response of rudder angle, and that in
Fig. 3 (b) is well progressed trapezoidal pattern.
Pattern in Fig. 3 (c)
can be seen as a damping pattern of
natural oscillation, and that in
Fig. 3 (d) is under progressing stage from triangular pattern to
trape-zoidal one.
11
In Fig. 7 response patterns of the system for course change in
waves obtained by simulation are shown.
These patterns resemble to
those of the tank test results
Pattern shown in Fig 7 (a) is thought
to correspond to that of Fig. 3 (a), and pattern in Fig. 7 (b) to that
of Fig. 3 (b).
The amplitudes and periods of response of tank test
re-sults correspond with those of simulation.
In Fig 8 (a) response for course change in calm water obtained
by simulation is shown. This system is stable and natural oscillation
has damped quickly in calm water. Fig. 8 (b) shows response pattern
of simulation of course keeping test 'in waves.
From these results it
is known that the natural oscillation of stable system in calm water
condition has been excited by waves even without course change (e=O).
Intuitively speaking mechanism how the natural oscillation is excited
by waves with the presence of the steering velocity saturation can be
explained by the redaction of effective steering velocity.
This
explana-tion seems quite reasonable from the following facts
First steering
velocity was almost saturated by the response for encounter waves and
there was only little margin left in the tank experiment, when the
feedback gains of the automatic steering system were large.
Second
it is known by simulation that reduction of steering velocity has
in-duced unstable oscillation in calm water condition.
Analytical method
based on the dual input describing function technique,'° shows
depend-ence of natural frequency of' the steering system on the exciting wave
height as observed in the tank test results.
In this analysis,
combina-tion of two non-memory type non-linear elements is treated as a memory
type non-linear element."
The existence of the memory type non-linear
element can explain the dependence of the natural frequency on the
wave height.
5. COMMENTS ON THE AUTOMATIC STEERING SYSTEM
IN THE SEAKEEPING MODEL BASIN
From the investigations described above, some improvements of
model test technique and specifications required for the automatic
steering system have been derived.
Gain constants for both proportional control k and rate
con-trol k2 should be smaller in waves than the optimum values in calm
water.
Cut off frequency of the low pass filter f. should be chosen
carefully not to make the whole system unstable.
Sthaller value of f,
reduces the stability of the systeth, through it is effective to avoid
useless steering of high frequency.
wave heights in tank tests are rather higher than those of actual sea
condition in which automatic steering devices are used.
Correspondence
of steering velocity between actual ship and model is not so important
in usual seakeeping test.
Therefore steering velocity should be as fast
as possible.
(4)
Because damping characteristic of the response is not so large
in waves as in calm water, angle of course change should be small in
the experiment.
6. CONCLUSION
The mechanism about unexpected long period response of
automa-tic steering system for ship model in the Seakeeping Model Basin has
been investigated.
From the results of analogue computer simulation,
the cause of the reSponse has been explained by the non-linear
charac-teristics of the system.
Some comments about the automatic steering
system and tank experiment have been obtained.
REFERENCES.
K. Sugai, H. Kitagawa, T. Fuwa and S. Ohthatsu: "Experimental Investigations into Impulsive Water Pressures upon the Hull Surface in Two-directional Irregular Waves ", Journal of the Society of Naval Architects of Japan, Vol. 138, 1975.
K. Sugai, K. Goda, H. Kitagawa, Y. Takei, M. Kãn, T. Miyamoto, S. Ohmatsu and
M. Okamoto: "Model Tests on Hydrodynamic Pressures acting on the Hull of an
Ore-carrier in Oblique Waves ", JiIrnal of the Society of Naval Architects of Japan,
Vol. 133, 1973.
H. Kitagawa: "Some Aspects of Ship Motions and Impulsive Wave Loads on an Ore Carrier Model in Two-directional Cross Waves ", Eleventh Symposium on Naval
Hydro-dynamics, LoSdon, 1976.
N. Mori, M. Kan and T. Miyamoto: "Study on Wave Loads and Transverse Strength
of Large Ore-carrier (7 )Automatic Course Keeping Test of Free Running Ship
Model ", Abstract Note of the 18th General Meeting of Ship Research Institute, 1971.
A. Ogawa and K. Otsu: "A Seakeeping Test on a Container Ship "America.maru"
on the North Pacific Ocean (Part 3) ", Report of Ship Research Institute, Vol. 9, No. 3,
1972.
T. Fuwa and T. Niura: "A Consideration on the Extraordinary Response of Model Ship's Automatic Steering System in Following Sea ", Collected Papers of the 26th
General Meeting of Ship Research Institute, 1975.
Y. Tákaishi, K. Sugai and A. Ogawa: "Recent Development in the Model Test Tech-niques in the Seakeeping Model Basin of the Ship Research Institute (1), (2) ", Bulletin of the Society of Naval Architects of Japan, No. 525, No. 526, 1973.
M. Shimura: "Non-linear Theory of Electronic Circuits ", Shoko-do, Tokyo, 1972. P. Boese: "Nichtlineare Einflusse auf das Steurn eines Schiffes im achterlichen Seegang ", Institute fur Schiffbau der Universität HamburgBericht Nr. 243, 1968.
J. E. Gibson: "Nonlinear Automatic Control ", McGraw-Hill, 1963.
T. Fuwa: "An Application of Dual Input Describing Function Method to the
PAPERS OF SHIP RESEARCH INSTITUTE
No. 1 Model Tests on Four-Bladed Controllable-Pitch Propellers, by Atsuo Yazaki,
March 1964.'
No. 2 Experimental Research on the Application of High Tensile Steel to Ship
Struc-tures, by Hitoshi Nagasawa, Noritaka Ando and Yoshio Akita, March 1964.
No 3 Increase of Sliding Resistance of Gravity Walls by Use of Projecting Keys under
the Bases, by Matsuhei Ichihara and Reisaku Inoue, June 1964.
No 4 An Expression for the Neutron Blackness of a Fuel Rod after Long Irradiation by Hisao Yamakoshi, August 1964.
No 5 On the Winds and Waves on the Nothern North Pacific Ocean and South Ad
jãcènt Seas of Japan as the Environmental ConditiOn for the Ship, by Yasufümi Yamanouchi, Sanae Unoki and Taro Kandà, March 1965.
No. 6 A code and Some Results of a Numerical Integration Method of the Photon
Transport EquatiOn is Slab Geometry, by Iwao Kataoka and Kiyoshi Takeuchi,
March 1965.
No 7 On the Fast Fission Factor for a Lattice System by Hisao Yamakoshi June 1965.
No. 8 The Nondestructive Testing of Brazed Joints, by Akira Kanno, November 1965.
NO. 9 Brittle Fracture Strength of Thick Steel Plates for Reactor Pressure Vessels, by
Hiroshi Kihara and Kazuo rkeda, January 1966.
No. 10 Studies and Considerations on the Effects of Heaving and Listing upon Thermo-Hydraulic Performance and Critical Heat Flux of Water Cooled Marine Reactors, by Naotsugu Isshiki, March 1966.
No. 11 An Experimental Inve&tigation into the Unsteady Cavitation of Marine Propel-lers, by Tatsuo Ito, March 1966.
No. 12 Cavitation Tests in NonUniform Flow on Screw Propellers of the Atomic,Power.
ed Oceanographic and Tender ShipComparison Tests on Screw Propellers De-signed by Theoretical and COnventiOnal Methods, by Tatsuo Ito, Hajime
Takaháshi and Hiroyuki KadOi, March 1966.
No. 13 A Study on Tanker Life Boats, by Takeshi Eto, Fukutaro Yamazaki and Osamu Nagata, March 1966.
No. 14 A Proposal on Evaluation of Brittle Crack Initiation and Arresting Temperatures
and Their Application to Design of Welded Structures, by Hiroshi Kihara and
Kazuo Ikeda, April 1966.
NO. 15 Ultrasonic Absorption and Relaxation Times in Water Vapor and Heavy Water Vapor, by Yahei Fujii, June 1966.
Nb. 16 Further Model Tests on FourBladed Controllable-Pitch Propellers, by Atsuo
Yazaki and Nobuo Sugai, August 1966. Supplement No. 1
Design Charts for the Propulsive PerfOrmances of High Speed Cargo Liners with C= 0.575, by Koichi Yokoo, Yoshio Ichihara, Kiyoshi Tsuchida and Isamu Saito,. August
1966.
No. 17 Roughness of Hull Surface and Its Effect on Skin Friction, by Koichi Yokoo, Akihiro Ogawa Hideo Sasajima Teiichi Terao and Michio Nakato September
1966.
No. 18 Experiments on a Series 60, CB=0.70 Ship Model in Oblique Regular Waves,
by Yasufumi Yamanouchi and Sadào Ando, October 1966.
No. 19 Measurement of Dead Load in Steel Structure by Magnetostriction Effect, by
Junji Iwayanagi, Akio Yoshinaga and Tokuharu Yoshii, May 1967.
No 20 Acoustic Response of a Rectangular Receiver to a Rectangular Source by
Kazunari Yámada, June 1967.
No. 21 Linearized Theory of Cavity Flow Past a Hydrofoil of Arbitrary Shape, by
Tatsuro Hanaoka, June 1967.
No. 22 Investigation into a Novel Gas-Turbine Cycle with an Equi-Pressure Air Heater, by Kösa Miwa, September 1967.
No. 23 Measuring MethOd for the Spray Characteristics of a Fuel Atomizer at Various Conditions of the Ambient Gas, by Kiyoshi Neya, September 1967.
NO. 24 A ProPosal on Criteria for Prevention of Welded Structures from Brittle
Frac-ture, by Kazuo Ikeda and Hiroshi, Kihara, December 1967.
No. 25 The Deep Notch Test and Brittle Fracture Initiation, by Kazuo Ikeda, Yoshio
Akita and Hiroshi Kihara, December 1967.
No. 26 Collected Papers Contributed to the 11th International Towing Tank Conference,
January 1968.
No. 27 Effect of Ambient Air Pressure on the Spray Characteristics of Swirl Atomizers, by Kiyoshi Neya and Seishiro SatO, February 1968.
No. 28 Open Water Test Series of Modified AU-Type Four- and Five-Bladed Propeller
Models of Large Area Ratio,
by Atsuo Yazàki, Hiroshi Sugano, MichioTakahashi and JuOzo Minakata, March 1968.
No. ?9 The MENE Neutron Transport Code, by Kiyoshi Takeuchi, November 1968.
No. 30 Brittle Fracture Strength of Welded Joint, by Kazuo Ikeda and Hiroshi Kihara,
March 1969.
No. 31 Some Aspects of the Correlations between the Wire Type Penetrameter
Sensi-tivity, by Akira Kanno, July 1969.
No 32 Experimental Studies on and Considerations of the Supercharged Once through Marine Boiler, by Naotsugu Isshiki and Hiroya Tamaki,. January 1970.
Supplement No. '2
Statistical Diagrams on the Wind and Waves on the North Pacific Ocean by Yasufumi Yamanouchi and Akihiro Ogawa, March 1970.
No. 33 Collected Papers Contributed to the 12th International Towing Tank Conference,
March 1970.
No. 34 Heat Transfer through a Horizontal Water Layer, by Shinobu Tokuda, February
1971.
No. 35 A New Method of C.O.D. Measurement Brittle Fracture Initiation Character-istics of Deep Notch Test by Means of Electrostatic Capacitance MethOd, by
Kazuo Ikeda, Shigeru Kitamura and Hiroshi Maenaka, March 1971.
No. 36 Elasto-Plastic Stress Analysis of Discs (The 1st Report: in Steady State of
Thermal and Centrifugal Loadings), by Shigeyasu Amada, July 1971.
No. 37 Multigroup Neutron Transport with Anisotropic Scattering, by Tomio Yoshimura,
August 1971.
No. 38 Primary Neutron Damage' State in Ferritic Steels and Correlation of V:Notch Transition Temperature Increase with Frenkel Defect Density with Neutron
Ir-radiation, by Michiyoshi Nomaguchi, March 1972.
No. 39 Further Studies of Cracking Behavior in Multipass Fillet Weld, by Takuya
Kobayashi, Kazumi Nishikàwa and Hiroshi Tamura, March 1972.
No. 40 A Magnetic Method for the Determination of Residual Stress, by Seiichi Abuku,
May 1972.
No. 41 An Investigation of Effect of Surface Roughness on Forced-Convection Surface Boiling Heat Transfer, by Masanobu Nomura and Herman Merte, Jr., December
1972.
No. 42 PALLAS-PL, SP A One Dimensional Transport Code, by Kiyoshi Takeuchi,
February 1973.
No. 43 Unsteady Heat Transfer from a Cylinder, by.Shinobu Tokuda, March 1973.
No. 44 On Propeller Vibratory Forces of the Container' Ship COrrelation between Ship
and Model, and the Effect of Flow Control Fin on Vibratory Foces, by Hajime
15
No. 45 Life Distribution and Design Curve in Low Cycle Fatigue, by Kunihiro lida and
Hajime lnoue, Ji.ily 1973.
No. 46 Elasto-Plastic Stress Analysis of Rotating Discs (2nd Report: Discs subjected to Transient Thermal and Constant Centrifugal Loading), by Shigeyasu Amada and Akimasa Machida, July 1973.
No. 47 PALLAS-2DCY, A Two-Dimensional Transport Code, by Kiyoshi Takeuchi,
November 1973.
No. 48 On the Irregular Frequencies in the Theory of Oscillating Bodies in a Free
Surface, by Shigeo Ohmatsu, January 1975
No. 49 Fast Neutron Streaming through a Cylindrical Air Duct in Water, by Toshimasa
Miura Akio Yamaji Kiyoshi Takeuchi and Takayoshi Fuse September 1976 In addition to the abOve-mentioned reports, the Ship Research Intitute has another
series of reports, entitled "Report of Ship Research Institute ". The "Report" is published in Japanese with English abstracts and issued seven times a year.
