A new scheme of a modified MAC-method is developed in order to analyse nonlinear waves named Free Surface Shock Wave around the bow of a 3-D floating body advancing steadily in deep water. The 3-D Navier-Stokes equations are solved by a finite-difference scheme under boundary conditions which are improved so that they suit the problem of nonlinear waves in deep water. It is shown that the computed bow waves around a bow are nonlinear waves which have the characteristics of free surface shock waves that have been experimentally analysed. The occurrence of free surface shock waves is theoretically demonstrated.
The nonlinear waves in front of a 2-D rectangular body are also studied both experimentally and theoretically.

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A modified Rankine source method is proposed, where the free surface condition is linearized based on the viscous-double-hull flow and the hull surface condition is approximated to be satisfied only by the double-hull potential. The flow field is represented by Rankine sources distributed over the free surface.
Preliminary pilot computations for 2-D and 3-D point sources are carried out in the first place in order to establish the computation scheme. Then the availability of the present method is exemplified by computing the free surface flows and the wave elevations of M-21 and Wigley model whose hull forms are so simple that their double-hull flows can be prepared with least numerical errors. In this first report we confine ourselves to the inviscid case.
The higher approximation for the discrete source density is certified to be significant. The employment of the approximation for the hull-surface condition decreases both computing time and memory storages so much that the present method is promising for practical purposes. Free surface flows and wave elevations are well reproduced as far as the two models are concerned.

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A new method of designing hull forms of minimum wave resistance is developed in which two major components of wave resistance, i.e., one due to free surface shock waves and the other due to linear waves are taken into account. A procedure of extracting wave profiles due to free surface shock waves is proposed, which is utilized as a quantitative measure of the magnitude of free surface shock waves. The relation between hull form and resistance coefficient due to free surface shock waves is empirically derived and it is incorporated into the wave-analytical procedure of obtaining hull forms of minimum wave pattern resistance, so that the sum of wave pattern resistance (linear wave resistance) and resistance due to free surface shock waves (nonlinear wave resistance) is minimized. The effectiveness of the new method is demonstrated by experiments.

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The characteristics of stern-waves generated by a deep-drafted model of simple hull form are experimentally investigated. The results show that nonlinear waves exist in the neighborhood of the stern and these waves are essentially same with free surface shock waves around bows in many respects except for the interaction with linear bow-waves and boundary layer. This interaction makes the stern wave formation more complicated having movement of starting point and change of strength. A simple calculation shows that the movement of starting point and attenuation of the stern waves remarkably influence the linear wave system in the far-field.

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In order to know the contribution of local hull geometry to the resistance of slow full ships, a calculation formula was derived to determine the resistance acting on the hull surface forward of an arbitrary transverse cross section. In determining the resistance use was made of the results of flow measurement at the transverse cross section outside of a ship model.
This formula was applied to the two full ship models whose wave resistances were negligibly small. The results of the calculation were found to agree with those based on a higher order boundary layer theory which takes into account pressure variation across the boundary layer. Resistance determined at the control surface right after a ship model was also comparable with towing test result.
Applicability of the present method was thus found to be promising, though there exists a room for improvement.

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The nonlinear programming 'SUMT' was applied to the hull form design problem with minimum resistance and Michell's theory was employed as wave resistance formula in the previous report. In the present report the low speed theory is introduced instead of Michell's formula. For the complexity of the formula based on the low speed theory, many approximate treatments must be used in the optimization process by SUMT. Numerical examples are given under the same constraints as in the previous report.
Model tests of hull forms designed by the procedures of 1st and 2nd reports involving the towing test and the wave pattern analysis are carried out to verify the validity of the hull form design method by means of nonlinear programming.

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The bodily sinkage of a ship going in shallow water is analysed by means of the analogy with the transonic aerodynamics. The OGSA method is employed to solve the basic equation in such a way that the nonlinear characteristic is preserved. The numerical work is confined in the subcritical speed range where a continuous solution exists. Three kinds of Wigley's parabolic models with different beam to length ratios are employed for numerical examples. Computed results for the sinkage show fairly good agreement with the measurement in the towing tank, and the feasibility of the method as the practical assessment of the sinkage in shallow water seems to be quite promising.

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In designing a ship, it is important to estimate the effects of the propeller-rudder interaction, as the rudder behind a propeller has a great effect on the propulsive performance of a ship. This interaction problem has been treated theoretically by applying the thin wing theory to the rudder, and the hydrodynamical forces have been discussed.
In this paper, the author develops the estimation method on the propellerrudder interaction by applying thick wing theory and boundary layer theory to a rudder with thickness. And then the forces, the velocity field, and the pressure on the rudder are discussed.

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Reaction fin is a device for improving propulsive performance of ships by providing preswirl to the propeller inflow for cancellation of rotation in the slipstream. This report describes the development of reaction fin for high block coefficient ships undertaken in Mitsubishi Heavy Industries, Ltd.
First, explanations are given on the effectiveness of reaction fin for full ships with some results from basic researches carried out in the early stage.
Next, development made on its practical application is described which includes studies on various aspects such as structure, vibration, monouevrability etc. as well as propulsive performance.
Finally, full-scale results are introduced from the results of the two ships fitted. with a reaction fin, showing that it is as effective as expected for improving propulsive performance without causing any troubles for service.

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This paper presents results of turbulence measurements in the three dimensional boundary layer and wake around a ship model in a low-speed wind tunnel. Measurements were carried out with a single channel hot-wire anemometer, where two or three types of probes were used to measure the different components of the velocity fluctuations.
The conclusions obtained in the present study are summarized as follows.
1) It is possible to measure the three dimensional mean flow, turbulence intensities and Reynolds shearing stresses by using a single channel hot-wire anemometer.
2) The three dimensional direction characteristics of a hot-wire can be approximately expressed by the following equation.
U_eff = |U| {sin²α+ a cos² α + b cos²β} ^1/2
where U_eff is the effective velocity.
α is the angle between the hot-wire and mean flow direction.
β is the angle between normal vector to the hot-wire/wire-support plane and mean flow direction.
a and b are the experimental constants.
3) In three dimensional boundary layer and near wake, the distributions of turbulence intensities are significantly affected by the velocity gradient and the bilge vortices.
4) Along a stern stream-line, as the boundary layer thickness grows thicker, the dimensionless eddy viscosity ε/U_eδ_* is more reduced.

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In the previous paper 1), authors presented the results of propeller open test, self-propulsion test and cavitation test (cavity extent and thickness) which were performed by using MAU type conventional propeller (MPNO. 80-3), conventional 90° Highly Skewed Propeller (HSP) (MPNO. 80-4) and theoretically designed 72° HSP (MPNO. 80-5).
They also described the outlines of simplified method to calculate Wake Adapted Skew Distribution (WASD) and non-linear lifting surface method to estimate propeller open characteristics which were applied to MPNO. 80-5 propeller design. The result of propeller open test reveals utility of non-linear lifting surface method for high efficiency HSP design.
In this report, the test results of fluctuating pressure induced by the above-mentioned three propellers and measured in cavitation tunnel are presented. Comparing with fluctuating pressure amplitude (1 st blade frequency component) of MPNO. 80-3, that of MPNO. 80-4 is reduced to about 57% and that of MPNO. 80-5 is reduced to about 12%, which reveals that skew distribution as well as skew angle significantly effects on fluctuating pressure and simplified method to calculate WASD is useful for HSP design.
Then, authors propose a practical method for calculating necessary skew angle to reduce propeller-induced fluctuating pressure amplitude to allowable level. The method is based on Holtrop's statistical method for predicting vibratory hull forces and Holden's criterion for fluctuating pressure amplitude. Recommendable skew angles indicated by examples of numerical calculation for eight ships are as follows ;
0°30° skew angle for bulk carrier
40°60° skew angle for pcc
50°70° skew angle for container

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In the previous papers 1), 2), authors presented experimental and theoretical data on propeller open characteristics, propulsive performance characteristics, cavitation characteristics and propeller-induced fluctuating pressures of MAU type conventional propeller (MPNO. 80-3), conventional 90° Highly Skewed Propeller (HSP) (MPNO. 80-4) and theoretically designed 72° HSP (MPNO. 80-5).
In this report, static stress on the blade of MPNO. 80-5 is first presented. The stress was measured under the condition that concentrated force was loaded at a point on the blade.
Principal stress measured is compared with that calculated by using the finite element method ; SPROSAS (Highly Skewed Propeller Stress Analysis System)¹²⁾ which was developed for this research project. Calculated results agree well with experimental values. The outline of SPROSAS is described.
Then, fluctuating stresses on the blades of MPNO. 80-3 and MPNO. 80-5 working in the wake of 7m container ship model are also presented. The stresses were measured at ahead, crash astern and astern conditions in towing tank.
Mean stresses for one rotation measured at ahead and astern conditions are compared with those estimated by using SPROSAS. Pressure distributions on the propeller blades are calculated by means of non-linear lifting surface methed.¹³⁾ Calculated mean stresses agree with experimental values for MPNO. 80-3. For MPNO. 80-5, calculated mean stress distributions on the propeller blade qualitatively correspond to those of experiment even though calculated mean stresses are smaller than experimental values.

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It is recently noticed that the non-uniformity of flow brings some deviation of the relative rotative efficiency from the unit and the difference of the effective wake factor from nominal one. The investigations are expected to enter in more details either experimentally or theoretically. The present paper is the report of the experiments and analysis works about the hydrodynamic characteristics of the model propeller acting in the wake flow of the alternate mesh screens of different patterns, such as some circumferential non-uniform wakes of the cos nθ function mode, a radial non-uniform wake and homogeneous wakes.
The measurements of velocity fields of cos nθ mode have shown the well correlation of the intensity of turbulence with the shear rate of the velocity profile along the circumference. From the results of the performance tests of the propeller behind the one or two uniform meshes screen, it has been found that the influence of turbulence of flow reduces the low Reynolds number effect of the model propeller. Accordingly, the characteristics of the model propeller in the wake of the two uniform meshes screen has been offered to apply to the analysis of the self-propulsion factor at any low Reynolds no.
It has been shown that the circumferential non-uniformity of the cos nθ mode, where n≤6, raises the efficiency of the propeller higher than that of the open condition, that is the high relative rotative efficiency over the unit. The results of analysis of data based on some theoretical considerations have allowed us to conclude that the relative rotative efficiency responds to the circumferential non-uniformity of flow nonlinearly and quasi-stationarily.

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This paper describes an estimation method of sheet cavitaion on a model propeller considering laminar separation of boundary layer. Existence of laminar separation at the leading edge is judged using pressure distribution calculation and two-dimensional boundary layer theory.
The sheet cavitation incepts when the pressure reaches below vapour pressure at the separation point. Then cavity extent in chord direction is estimated combining linear cavity theory and lift equivalent method.
The estimated cavity extent agrees well with the experiment except when the cavity is at a growing condition in wake. In this case, transient effects of the separated region and cavity bubble formation seem predominant and the observed extent is sometimes much smaller than the calculated result.

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It is well-known that sheet cavitation inception is dependent on laminar separation. Therefore, the sheet cavitation might be controlled by restraining the separation.
Authors tried to control sheet cavitation on an axisymmetric body by water jet injection, and proved experimentally that it was possible to suppress the sheet cavity.
The nondimensional injection flow rate for the cavity suppression depended only on Reynolds number. The leading edge of the sheet cavity coincided with separation point which was visualized by oil film method. By increasing injection rate the reattachment point of separation bubble moved upstream and finally the separation bubble vanished. The sheet cavitation also vanished at the same condition.

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This paper gives a general description of the Marine Propeller Cavitation Tunnel which was built at the Department of Naval Architecture, the University of Tokyo in March, 1980. First the basic design concept on a cavitation tunnel is stated with emphasis on the importance to keep air content of water adequately.
The tunnel has two interchangeable test sections. The propeller test section has a square cross section of 0.45m×0.45m. Maximum water velocity in this section is 11.2m/s. Another test section, the foil test section has a rectangular cross section of 0.60m×0.15m. Its maximum water velocity is 19.5m/s. Minimum and maximum absolute pressures in both sections are 0.1 and 3.0 bar, respectively.
A series of cavitation test on a model propeller was made at various revolutions, static pressure and air content to demonstrate the importance of air content control. The measurement of tiny air bubbles, which act as cavitation nuclei, was also performed by a scattered light counting instrument.

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The floating-body forms having two frequencies at which no heaving force is exerted in waves are considered in this paper. It is found by applying Chou's method that the floating-body forms possess the constricted part between the free surface and the bulbous part in the water. Heaving forces of several cylinders with the cross sections of the wave-free forms are calculated by source method and measured in wave-excitation experiments. Both results of the calculation and the experiment confirm that heaving forces vanish at two frequencies.
Secondly, investigations are made for a catamaran composed of such cylinders and a vertical body of revolution whose profile is similar to the cross section of one of the cylinders. It is also the case for these bodies to have two wave-free frequencies.

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The hydrodynamic effects of the angles of the intersection between hull-side and the freesurface, so-called the Wedge-effects are investigated in the two-dimensional radiation and diffraction problems. First and second-order forces by the regular perturbation theory are calculated for two bodies which have the same beam/draft ratio and the sectional area, one intersects at right angles at free-surface, and the other does at a half of right angles.
Experiments in forced heaving and swaying oscillations and the diffraction problem are carried out and compared with the calculations.
Obtained results summarize as follows.
1) First-order hydrodynamic coefficients are not affected very much by the Wedge-effects to the extent of a half of right angles.
2) Second-order vertical forces are affected significantly by the Wedge-effects, but horizontal forces are affected little.
3) The Wedge-effects can be explained as the oscillatory change of wetted-surface and the experimental results agree well with the calculations.

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In order to evaluated the response of motion of an arbitrary shaped body with a constant forward speed in waves, the hydrodynamic forces and moments acting on it have to be predicted accurately. The strip method has been usually applied to obtain these hydrodynamic forces acting on a ship shaped body, where the two dimensional hydrodynamical characteristics of each cross section are used. However, the strip method has some deficiencies arising from the fact that the effect of the forward speed can not be considered rationally, and that some three dimensional effects are not taken into consideration.
The author developed the method to calculate the three dimensional hydrodynamic forces and moments acting on an arbitrary shaped body with a constant forward speed, in which the sigularities are distributed on its surface, with an intention of investigating the effect of the forward speed as well as some three dimensional effects on the hydrodynamic characteristics.
For a half submerged elliptical model with a constant forward speed, the sigularity distributions of diffraction and radiation problems were determined by this calculus. Wave exciting forces, wave pressure distributions on its surface, added mass and damping coefficients were calculated by this method and compared with both the experimental values and ones calculated by the strip method.

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A theoretical derivation is presented for the radiation problem of an oscillating slender ship, moving with forward velocity in calm water.
Assuming thatU=0 (ε^1/2), and that ω=0 (ε^-1/2+a) (0<a<1/2), the linearized boundary conditions are derived in the outer and inner regions respectively. The solutions of each region are matched to determine the unknown source strength and the homogeneous component in the inner solutions, according to the interpolation slender body theory.
Computations and measurements are carried out for the added mass and damping coefficients of a slender ship model, with cross sections defined by Lewis forms.
Comparing the results, it appears that the present method gives good predictions, including the contributions from forward velocity and the interactions between sections along the length.

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The vertical bending moment in following sea to be calculated by Strip Methods has an important problem as obviously shown in the results of the international joint calculation under the Seakeeping Committee of I.T.T.C.
In this paper, for the first time, the following Transient Water Wave was adopted in experiments. As the results suggested, good data was obtained effectively, and the fact that Transient Water Wave is useful even in following sea conditions was proved. Next, a practical method of calculation taking into account three-dimensional correction is presented. By applying this method, experimental values of vertical bending moment in following waves at near -zero encounter frequency can be explained satisfactorily.

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When a ship is travelling in a following sea, of which the wave length is almost twice the ship's length, with an advance speed nearly equal to the wave celerity, the ship is violently turned against the helm of rudder. This phenomenon is called the broaching-to, and feared by the seamen for a long time. There exist some different notions as regards the immediate cause of occurrence of this phenomenon. The widely supported notions are as follows a) reduction of rudder effectiveness in the following seas, b) instability of course keeping of a ship travelling on the downhill slope of wave, and c) the action of turning moment due to the cross flow component of the orbital motion of water particle.
In this paper, the authors discuss the propriety of the traditional notions stated just above by examining them with the hydrodynamic data obtained from the restrained model tests. As a result of the examination, the authors conclude that any of the above stated causes is. not the immediate cause of occurrence of the broaching-to phenomenon.
In order to understand the characteristics of the ship motion travelling in a following sea, a simulation study of surge, sway and yaw motions is executed. As the result, it is found that the violent turn of a ship travelling on the downhill slope of the following wave is excited by the wave turning moment when the ship has an advance speed equal to or slightly lower than the wave celerity, and moreover the encounter angle of the ship to the wave is around 20 and 30 degrees.
Consequently, the authors conceive that the broaching-to phenomenon occurs when the wave exciting yaw moment becomes remarkably high compared with the hydrodynamic moment of course keeping generated by the helm of rudder. This notion is verified by analysis of the broaching-to phenomenon observed at a full-scale experiment in the sea.

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Using a radio controlled model, the experiment succeeded to realize broaching-to phenomena on a small high speed boat in the model basin stably.
The broaching-to always occurs when the ship is under surf-riding condition on the front slope of waves and the velocity of ship reaches to almost the same as that of the wave propagation. Through the parametric tests, it was made clear that the most likely conditions are λ/L=2.0, χ=20°-30° and Ucosχ=V_w.
Many items of measurements were conducted and behavior of the model ship during the broaching-to was recorded. In order to analyse the brcaching-to phenomena, the AIC evaluation technique was applied to the problem. As the result, the optimal form of the manoeuvring equations was derived and each coefficient was identified. Dynamic balance of each component in broaching condition was discussed.
Experimental results in the model basin were compared with those of the ship in seas during the broaching-to. It was recognized that both records were similar in pattern and agreed well in quantity.

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Digital simulation of maneuvering motions and numerical calculation of directional stability indices are carried out on the basis of captive model test of a typical container ship. An emphasis is laid upon yaw-sway-roll-rudder coupled motion. The smaller metacenteric height proved to introduce the better turning performance and the poorer course-keeping characteristics.
The yaw-sway-roll-rudder coupling can be a cause of anomalous rolling which is frequently observed at automatically steered, high speed operations in seaways. We introduce a perturbation stability analysis on the problem. It reveals the possibility of an unstable yaw-roll behavior due to roll-induced yaw moment, small GM and inadequate control parameters of autopilot steering system.

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Among various aspects of manoeuvrability of ships, steerability in wind, wave, and current is one of the vitally important problems, because it is directly related to the safety of ship handling. To this steerability, rudder operations for course keeping, which are usually called as “check helms”, are closely related.
Investigation was made, therefore, on a calculation method of check helms for course keeping under steady external forces. This method is derived so as to fully utilize captive model test results for assured reliability.
As an example ship form, a liquified natural gas carrier (LNGC) was examined. With the results of captive model tests, check helms and drifting angles were calculated for various design requirements which include estimation of the effects of rudder area and drifting forces due to wind and wave, together with their full-scale prediction. And it was shown that the present method is one of the practical and useful calculation methods.

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In the previous papers, a set of fundamental equations of motion for a submersible was derived in order to analyze the motion characteristics, and the relationships between the motion characteristics and the design parameters were investigated.
This paper deals with the research on the relationships between control system structure in longitudinal motion and design parameters of the submersible, that moves at constant speed along the orbit where a series of measuring points is prescribed. First, the state equation in the longitudinal direction suitable for the body design is derived. The control system of the submersible is provided. Quadratic function is defined so as to estimate the control performance of the motion. Finally, the kind and the range of design parameters are determined from the engineering standpoint.
The main results are obtained as follows.
(1) Even if a sudden change of the direction of water current occurs consistently, the submersible can be controlled to move along the demanded orbit by utilizing a regulator composed of the state variables.
(2) The state equation can be decomposed in two parts ; one is the equation expressing surging motion, and another the equation expressing both heaving and pitching motions if the submersible design is satisfied with conditions for improvement of idealized controllability.
(3) 15 design parameters are derived from the coefficients of the state equation.
(4) The submersible which is designed symmetrical around the body axis is controllable to the large extent of deformation.
(5) The control system is lack of observability, in the case that nondimensional time constant of the steering apparatus is approximately 2.1.
It is concluded that the method to obtain the relation between the design of submersible and its performance applying to the optimal control has been established and that the indispensable knowledge to quantitatively evaluate various kinds of submersible has been provided.

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This paper presents both theoretical and experimental studies on evaluating dynamic responses of the moored object and the mooring lines in regular waves. This time domain method treats the mooring line as lumped parameter system of discrete masses and considers the mutual interaction of dynamic response between the moored body and the mooring lines. Numerical results for the motions of the moored body and the dynamic mooring tensions were obtained and are compared with experimental data with excellent agreement.
As a result of this study, it is found that the dynamic effect on the mooring tension is significant when the floating body is moored and may influence on the body motion considerably unless the body is large enough in size. Secondly, the effect of this dynamic tension on the moored body motions becomes large comparing with that of the nonlinearity of the mooring restoration in case that the mooring line is heavy. Therefore, it is concluded that the dynamic analysis of the mooring line is important for the analysis of the moored body motion and for the design of the mooring system.

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As attention paid to development of oil and gas in deep waters has increased, various kinds of concepts of compliant structures have been correspondingly proposed as the production platforms. Among them, the guyed tower and the taut moored platform (also called as the tension leg platform, hereafter abbreviated as TLP) are considered the most expectant at the present time. The first actual one of each type of these structures is planned to be installed a couple of years later.
Authors have carried out several series of two dimensional wave exciting tests on small scale TLP models and have developed the analysis methods for the phenomena observed at the wave exciting tests.
In this paper, three dimensional wave exciting tests were carried out by using a small scale model in regular waves with variable wave angle. The linear response analysis program in the frequency domain and the nonlinear response analysis program in the time domain were developed in the three dimensional case. Comparing the experimental results with the calculated ones, the characteristics of the three dimensional responses and the nonlinear phenomena are discussed.

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In this paper the authors investigate the vortex-making damping forces of a column with a circular footing, varying its depth. Further, the motions for one model in waves are measured and compared with those estimated by a linear potential theory. It is found that the amplitude of the heaving motion is smaller than the linear calculation in the resonant oscillation, but in contrast it becomes finite at the wave-excitationless frequency.
In order to improve such estimations, the vortex-making effect is taken into consideration not only in the damping forces but also in the wave-excitation forces. The linearised vortexmaking damping coefficient is constant for the smaller amplitude of oscillation, and is quite larger than the wave-making damping coefficient. Further, it increases with the amplitude when the amplitude ratio becomes greater than a certain value. Therefore, the heaving motion in resonance reduces very much and the calculation shows a good coincidence with the experiment. In addition, it is assumed that the wave-excitation force is also affected by the vortex-shedding at the footing. This effect becomes important at the wave-excitationless frequency where the excitation force may otherwise be zero, and the finite heaving motion can be well explained.

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In the design of a floating oil storage system, especially of its mooring system, it is essentially important to accurately estimate the environmental forces.
In order to evaluate the design values of wind loads, the characteristics of wind such as storm frequency, spectrum of fluctuating wind at the site were investigated based on the results of meteorological observations. Further, characteristics of wind loads such as the influences of shape of barge and hydrodynamic mutual interaction with adjacent barges were examined in detail by wind tunnel tests.
As the results, the design values of the wind velocity and the wind drag coefficients were obtained with sufficient reliability by taking the above-mentioned factors into consideration.

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It is presented how to analyze the wave power absorbed in irregular waves by using both its spectrum and its probability. Absorbed wave power in irregular waves consists of steady component and fluctuations. Both the former and the spectrum of the latter and further the probability density function are derived from a wave spectrum, a transfer function of the motion and characteristics of a load system for general cases in which the load system includes not only damping component (“resistance”) but also spring component (“reactance”) in reaction torque. Comparisons of experiments with the theories about a Salters Duck confirm the utility of this analysis. This analysis can be applied to other floating type wave energy absorbers besides a Salters Duck. It is also presented that an accumulator of a hydraulic device of a load system works very effectively for smoothing the fluctuations of absorbed wave power in irregular waves.

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A series of tank tests for slamming was carried out in the seakeeping basin, making use of an elastic ship model. The flexural rigidity of the model were reduced according to the laws of similitude. In this paper, foamed vinyl chloride was chosen for the material of the model. This material, which has relatively low modulus of elasticity and large damping for vibrations, is one of the best candidates for clarifying the characteristics of whipping vibrations caused by respective slams.
The experimental results are compared with the nonlinear theory proposed by the authors in the previous papers, which shows good agreements.

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In this paper, authors estimate long-term distributions of wave induced bending deflections of three ships including a dry cargo ship, a bulk-carrier and a destroyer. The extreme values in the long-term distributions of midship deflections, the probability of exceeding the value is equal to 10^-8, range from L/1000 to L/500. The values are larger than those in still water which are expected to be smaller than L/1000 in usual case from a result of measurment on 28 ships, which have length from 120 m to 160 m and belong to the same group as the above three vessels in their size. It is also remarkable that the values scatter widely.
Authors study on the character of the extreme and clarify that design wave bending stress, ship length, ratio of ship length to depth, fineness of hull form, and structure type have effects on the deflection. So it is impossible to keep the deflection in a range by keeping only design stress in a given value.
From the study authors develope a method of estimating the extreme midship deflection with very small erorr provided the extreme value of wave induced bending moments is known. And in appendix authors show an improved method of calculating bending deflection at midship from values of bending moment at three positions which divide ship length into four equal parts.

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Long term fullscale measurements of a container ship (24, 000 t DW type) on the PNW (Pacific North West) course have been operated for 52 months. Measurements and recordings have been conducted automatically using an automatic RMS meter which was developed by the authers. For three items of pitching angle, rolling angle and wave bending stress of upper deck, the RMS values, the maximum peaks, the minimum troughs and the zero cross mean periods for 30 minutes have been punched out in every three hours. The environmental condition data by the favor of the ship's crew are to be studied comparing with those ship's responses.
In this first report, the authers have studied the statistical distribution of the environmental conditions, and corresponding operating conditions specially in rough seas. The number of data of the rough sea condition of wind velocity ≥40 kt or wave height ≥5 m, were about 400 among the 5, 200 total data.

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In this paper a summary of results is presented of full scale measurements on a LPG carrier of semi-membrane tank type which have been carried out for about two years during her voyage between Japan and the Persian Gulf.
The unmanned measurements have been made on dynamic loads caused by liquid sloshing in a LPG tank of a restricted cargo filling ratio of either over 90% or below 30%. The test includes also measurements of reaction forces acting on a tank dome supporting the tank at upper deck structure. Long term measurements of ship notion as well as stresses due to longitudinal bending of hull girder have also been carried out. A statistical study has been made on a relationship between the ship motion and the frequency of occurrence of the liquid sloshing in LPG tank.
The results of the measurements have been compared with results of bench test on liquid sloshing in model tank in order to investigate into the effect of tank size on the magnitude of impact load due to sloshing.

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Recently shipbuilders in Japan have designed and constructed many jack-up oil rigs, and accordingly quite a few investigation have been performed on the static and dynamic characteristics of jack-up oil rig.
The authors have been systematically studying not only the global vibration of oil rig, but also the local vibration of leg by theoretical and experimental approach.
In the previous paper, the authors mostly discussed the calculation technique and pointed out the spring effect of the sea bed is very important factor for calculation of natural vibration of oil rig.
This paper deals with the vibration tests of the actual jack-up oil rig constructed during two years. At these tests oil rigs were excited by “Wire cutting method” to measure the lower natural frequency and logarithmic decrement. At the same time, the vibration of leg to wind excitation was also measured to catch its natural frequency.
Main conclusions are as follows :
(1) “Wire cutting method” is very useful for measuring natural frequency and logarithmic decrement of oil rig.
(2) The measured lower natural frequencies are approximately proportional to h^-3/2 (h : platform height) and W^-1/2 (W : platform weight).
(3) Logarithmic decrement shows from 0. 2 to 0. 3, which is larger than ship's.
(4) The first and the second mode of the leg are governed by bending and torsional deformation, respectively. The former natural frequencies are approximately proportional to l^-2 (l : leg length) and l^-1, respectively.

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The design concept of ocean structures is now changing from the “design by rules” concept to the “design by analysis” concept, where starting from load analysis, various kinds of analysis such as stress analysis and failure analysis are carried out in a same flows. And it can be also pointed out as a special feature of the “design by analysis” that safety of structures is estimated from probabilistic point of view instead of the decisive estimation which has been adopted for long time.
In the case of probabilistic estimation of structual safety, it is necessary to handle the two kinds of probability, the probability of structural strength which is originated from randomness of external loads, and the probability of material strength caused by scatterness of material qualities. And in the present report, the former problem is investigated mainly.
In order to investigate probabilistic problems of the structural strength, it is firstly required to know stochastic characteristics of external loads, wave loads in case of ocean structures, and working stress induced by the loads. Therefore the stochastic pattern of working stress under wave loads is studied mainly experimentally, based on an experiment carried out for two years using a ship on service. Then, taking the stochastic characteristics of working stress into consideration, strength of fatigue strength which is regarded as a most usual mode of failure is investigated from stochastic point of view. Finally the results obtained are compared with the results presented in such codes as BS and AWS.

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In the previous report, the authors carried out impact test and a milling test by use of a propeller model designed for a high powered icebreaking merchant ship of Arctic Class 7 and above and made clear propeller ice loads in various prepeller-ice interacting conditions.
In this report, the authors study the behaviour of stresses caused to the propeller by these ice loads by carrying out a static load test using FPP and CPP models of 1.1 m diameter and also FEM analysis. From this, the authors experimentally and theoretically clear stress level and strength order of each component of the propeller and obtain useful data for designing propellers for ice breaking merchant ships. At the same time, problems concerning application of FEM in development of such propellers are found.

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Static flexural tests were carried out on three types of ferrocement ; type A and type B to DnV rule, and a type with reinforcement only in tension side. Reinforcement content was systematically changed for these three types. Strength of ferrocement plate such as elastic modulus, cracking moment and maximum flexural moment were discussed assuming the ferrocement plate as a composite beam of mortar and steel, while ferrocement is assumed as a uniform material in many papers.
Flexural moment, flexural elastic modulus and average crack spacing were discussed in terms of content and specific surface of reinforcement.
Following conclusions were obtained ;
(1) Flexural strength can be estimated on the basis of strength of mortar and reinforcement.
(2) The moment at which cracks 0.02 to 0.025 mm wide are observed is about one and a half times of the estimated on strength of mortar.
(3) From strength view point, optimum value of specific surface of reinforcement exists for structures of ferrocement of type A. For the value, cracking moment and maximum flexural moment are correlated to thickness of ferrocement plate, irrespective of type of structure.

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A practical method of overall finite element analysis of a ship structure is proposed by the present author basing on the theory of a thin-walled beam in 1971. This method was proved to be useful in the initial design of the ship hull.
Effects of the shear deformation as well as the warping-torsion of the ship, however, were not completely taken into account in this analysis.
In 1976 he proposed a family of new discrete elements entitled the Rigid Body-Spring Model (abbreviated as RBSM) which were proved to be powerful in the limit analysis of solids and structures. It was found recently that this beam bending element can take into account influences of the shear deformation as well as warping torsion successfully. In this paper theoretical basis of this beam element is introduced first and then introduction will be made on a method of the discrete limit analysis of a ship structures idealized as a thin-walled beam with the variable cross section. And finally a practical method of the realistic ultimate strength analysis of a ship structure will be discussed.

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The Rigid Bodies-Spring Models (as abbreviated RBSM) proposed by Kawai in order to generalize the well-known method of plastic analysis from a viewpoint of the discrete analysis have been applid to various types of nonlinear structural problems and their validities have been sufficiently demonstrated. It is a great contrast to the conventional finite element method that these discrete elements were developed for the main purpose of evaluating the ultimate strength of structures, so that the structural analysis by using the RBSM may be called the Discrete Limit Analysis.
The physical concepts of the RBSM were definitely explained by Kawai in his literatures, but the algorithms for the application of the RBSM to arbitrary thin-walled structures were not necessarily obvious. Recently one of authors Toi has carried out the formulation of a series of rigid element models for shell structures and established the analytical procedure for these structures including arbitrary shells.
In this paper the general formulation of curved rigid element models is carried out for the discrete limit analysis of shell structures whose middle surfaces are defined as the coordinate surfaces of the orthogonal curvilinear coordinate systems, following the physical concepts of the RBSM for the plate bending and plane strain problems. This general formulation is applied to circular cylindrical shells and some numerical results are shown. The present analytical procedure for circular cylindrical shells may be considered as the extension of the generalized yield line method developed by Sawczuk and Janas from the standpoint of the discrete analysis.

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Discontinuous parts of steel structure, such as ship construction may be subjected to stress-es exceeding yield point which cause plastic deformations and cracks on occasion due to over loads arisen from waves etc..
To make clear the strength of such structure, the elasto-plastic analysis by means of finite element method is often employed. For one half cycle loading analysis, the method of Yamada et al. is well known as adequate one for practical application.
However the method of analysis based on three dimensional stress-strain law of a material which is able to simulate its behavior including the effect of arbitrarily varied loading cycles taking Baushinger effect into account has scarcely been proposed.
Authors present a method of analysis which deals with such objects, using an anisotropic hardening model by means of yield surface theory to obtain the constitutive equation, employing a simulation algorithm developed by one of the authors et al. for uniaxial loading which is capable to predict the stress-strain behavior of steel subjected to arbitrarily varied loading cycles.
This method was applied to the analyses for ductile fracture problem and the prediction of plastic fatigue endurance of steel structures.

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The experiment and the analysis by the use of finite element method were carried on to study the local strength of the deck plate subjected to the large wheel load such as that of ferryboat, car-carrier and Ro/Ro ship. In studying, it is assumed that those deck plates can be regarded to the rectangular plate loaded with partially distributed pressure.
(a) Experiment
The steel plates used in the experiment were square with side length 800 mm and 2.0, 2.3, 2.6, 2.9, 3.2 and 4.5 mm in thick.
The tested plate was divided in three panels having 200 mm in width, 600 mm in length by supporting walls when the plate was fastened to testing apparatus. The behavior of the central panel was investigated.
The plates were tested in two ways of loading. In the first, the load was increased continuously and in the second, as shown in fig. 8, the load was incresed under repeating the process combined of loading, unloading and reloading.
We obtained the various behaviors of the panel, especially the pattern of the residual deflection after the load had been removed, and found the fact that the panel do not produce the collapsing due to forming the plastic hinge lines.
(b) Analysis
The calculated results were approximately consist with the experiment. It is shown that the behavior of the partially loaded panel can be predicted by finite element method.
(c) Proporsal for design
In can be considered that the deck plate subjected to large wheel load designed according to NK rule have the suitable scantling, but the method of designing on the basis of the actual behavior of the panel may be more reasonable than that assumming the plastic collapse.

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Welding deformations and residual stresses are major factors which affect the collapse strength of externally pressurized vessels. Problems of circumferentially welded cylindrical shell and spherical shell welded along the equator have been already investigated by some of the authors.
There are many cases that a penetrator or a partial sphere is welded circumferentially to a spherical shell in actual structures. In this case, the spherical shell near the weld line and the penetrator tend to sink toward the center of spherical shell.
In the previous paper, the deformations of a spherical shell caused by the welding of penetrator were investigated. Experiments were carried out in order to clarify the characteristics of welding deformations and the effects of shell and penetrator dimensions and welding procedures on them.
In this paper, one dimensional thermal elasto-plastic analysis using Rayleigh-Ritz method is applied to the axi-symmetric thermal stress problems of thin spherical shells. The following conclusions are obtained from this analysis. The effectiveness of this analytical method and reliability of its results are confirmed by comparison with the experimental results. The influence of size of spherical shells and penetrators and welding heat input on welding deflections and residual stresses is described. It is clarified that the parameter λ and λα, which correlate the rigidity of shell and the size of penetrator, and the parameter (Q/h) β, which correlates welding thermal cycle, are effective to estimate the welding deflections. The deflection caused by the welding of penetrator shows maximum value when the size of penetrator λαequals 0. 71. 3, and this value is three times as large as that by the welding along the equator, and as the size of penetrator λα is larger than 4. 05. O, the welding deflection is almost the same as that by the welding along the equator.

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In our previous papers, assuming that fatigue crack propagation is continuous fatigue crack initiation at the crack tip, a model for fatigue crack propagation was presented. And for this model, an equation for calculating the crack propagation rate was derived in terms of stress intensity factor, effective stress range ratio and material properties such as Young's modulus, yield strength in strain cycling, strain-hardening exponent in strain cycling, Manson-Coffin's exponent, etc.
In this report, effect of fatigue crack closure phenomenon on the crack propagation rate is investigated experimentally, and relation between effective stress range ratio U and stress ratio R is given for mild steel. Further more, effect of the material constants on the propagation rate is also studied based on the above equation.
Experimental values of crack propagation rate on various stress ratio obtained by authors and several investigators are compared with calculated ones, and fairly good agreement between them was found.

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In the present paper, authors have performed an experimental study on fatigue crack propagation at threshold level to clear the effects of stress ratio and stress history upon the threshold stress-intensity factor (K-threshold). Fatigue tests were carried out under load controlled three-point bending condition using side notch type specimens.
The K-threshold values under the different stress ratio conditions are obtained by load decreasing test method which can eliminate the influences of loading history. The results show that the K-threshold range decreases with the increasing of stress ratio. An empirical equation which represents the relation between K-threshold range and stress ratio is proposed based on the comparison among present results and other researchers' data.
TheK-threshold values after crack propagation at constant stress range are obtained by load increasing test method under various stress ratio conditions. It is found that theKthreshold value after stress history increases with the increasing of stress range at stress history process. And this tendency is well characterized by using maximum stress-intensity factor at stress history process and at threshold. A simplified equation for the prediction of K-threshold value after given stress history of constant stress range is derived from the present study. Estimated K-threshold values by proposed equation show fairly good agreements not only with present results but also with other researchers' data.

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Recently the fracture mechanics analysis is often used as a means to verify the structural safety and soundness. In making the fracture mechanics analyses, the existance of crack should be firstly assumed and then the growing behavior of the crack is calculated and predicted. Most of the characteristics of the crack behavior are theoretically analysed and experimentally confirmed, however, some of the else are expediently assumed by the lack of the informations. One of these uncertainities, for example, is the fatigue crack path which have propagated toward the fillet weld line on the plates intersections.
In these circumstances, the authors investigated fatigue crack propagation behaviors at fillet weld on plates intersections, by conducting I-shaped section beam bending tests and stiffened plate tensile tests. And they tried to characterize the fatigue crack path in relation to the crack attack angle to weld line, the weld leg length, the flange stiffness and so on.
Resulting from the experiments, it has been verified that cracks propagate almost exactly to the normal direction to the maximum principal stresses before the crack tip reaches to the weld reinforcement.
And when the crack tip comes to the weld line, it can be roughly classified by several parameters whether the crack goes across the flange plate or turns its direction and goes along the weld line. Namely, the experimental chart to estimate fatigue crack path was obtained using the maximum principal stress at crack arrival point on weld line and the shearing stress along the fillet weld throat section.

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In the previous study, the authors have discussed the fatigue strength of load-carrying fillet welded cruciform joints with no-penetration having critical leg-length proposed by Gurney, and it was found that the mode of failure were classified into three types of failure : weld failure, mixed failure and plate failure.
In this study, an improvement of the fatigue strength was examined by fatigue tests under pulsating tension using the fillet welded cruciform joints of which the penetration was 5 mm in depth and other configurations were same as the cruciform joints used in the previous study.
As a result, the following conclusions were obtained.
(1) Change of the mode of failure in fillet welded cruciform joints can be explained by the estimation of the crack initiation life at weld toe, N_c^T, the fracture life of plate failure, N_f^T, and the fracture life of weld failure, N_f^T.
(2) In as-welded cruciform joints used in this study, the effect of retardation of crack propagation from the weld root can be expected due to the residual compression stress near the weld root.

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Low cycle fatigue crack growth behavior of 2 1/4 Cr-1 Mo Steel is investigated under fully reversed strain control at room temperature for center cracked specimen. Application of the cyclic J-integral (ΔJ) approach is attempted.
Experimental results for center cracked specimen under fully reversed strain control are also compared with those for center cracked specimen and CT specimen under slop line control, and those for CT specimen under load control.
It is known that ΔJ is a successful parameter for low cycle fatigue crack growth and the estimation of crack opening behavior rather than crack closure behavior is important for the improvement of accuracy under fully reversed strain control.
It is important to verify the crack growth estimation by the experimental data in application of ΔJ to structural components, therefore some investigation is made for the prediction of low cycle fatigue crack growth in center cracked specimen.

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Hysteresis loops were recorded intermittently but periodically during completely reversed, strain-controlled low cycle fatigue tests of four kinds of steel : a mild steel and three high strength steels. The longitudinal strain amplitude ε_±a was controlled over the gauge length of 12.5 mm on 8 mm diameter test section of the smooth, solid cylinder type specimen. After the conversion of the loops to true stress versus natural strain hysteresis loops, cyclic characteristics were studied on true stress amplitude, hysteresis energy and hysteresis loop shape.
Main conclusions obtained are as follows :
(1) The transition strain amplitude ε^*_ta, on which neither cyclic hardening nor cyclicsoftening is occurred, is expressed as a function of ultimate tensile strength σ_u (kgf/mm²).
log ε^*_ta =0.0478 σ_u -4.544
(2) Although plastic strain hysteresis energy per cycle ΔW behaves irregular and remarkable change in the beginning stage of cycling, that is approximately less than 2 percent of the crack initiation life, the change of ΔW is neglegible order after the beginning stage.
The fatigue toughness W_f (kgf/mm²) is expressed as a function of ultimate tensile strength σu and visible crack initiation life N_c.
W_f= (94.93-0.347σ_u) N_c^0.335
(3) The ratio of ΔW to the product of true stress range and plastic strain range is not constant during the fatigue cycling, and the mean value of the ratio over the total cycling for a specimen is expressed as a function of the total strain amplitude.
(4) The constants a and n in the n-th power strain hardening formula are expressed as a function of N and ε_ta for the nearly total range of cycling excluding the beginning stage.
An empirical formula was found between a and 1/n.
1/n= (log a+1.623+0.376log σ_u)/(0.1539-1.169 logσu)
(5) An estimation procedure for crack initiation life was proposed on the basis of the fatigue toughness, showing an estimation error less than 28 percent.

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