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The Specialist Committee on Stability in Waves Final Report and Recommendations to the 25th ITTC

1. INTRODUCTION • Professor D. Vassalos (until 2006), Ship Stability Research Centre, UK The committee would like to acknowledge 1.1 Membership and Meetings the valuable contributions of experimental and simulation data to the benchmark studies from Membership. The Committee appointed the following universities and research estab- by the 25th ITTC consisted of the following lishments: Helsinki University of Technol- members: ogy (TKK); Marine Design and Research • Dr. N. Umeda (Chairman) Institute of China (MARIC); Maritime Re- Osaka University, Japan search Institute Netherlands (MARIN); Mari- • Mr. A. J. Peters (Secretary) time and Ocean Engineering Research Institute QinetiQ, Haslar, UK (MOERI); National Technical University of • Professor S. Fan Athens (NTUA); Ship Stability Research Marine Design and Research Institute of Centre (SSRC), Osaka University; Instituto China Superior Tecnico (IST); the EU project • Professor A. Francescutto SAFEDOR; and the Office of Naval Research. University of Trieste, Italy Meetings. Four Committee meetings were • Dr. S. Ishida, held as follows: National Maritime Research Institute, Japan • Osaka, Japan - March 2008 • Dr. J. O. de Kat (until 2006) • Gosport, UK - May 2007 Maritime Research Institute Netherlands • Rio de Janeiro, Brazil - September 2006 • Professor A. Papanikolaou • Wageningen, NL - February 2006 National Technical University of Athens, Greece • Dr. A. M Reed 1.2 Tasks from the 24th ITTC Naval Surface Warfare Center, USA • Dr. F. van Walree (from 2007) • Develop a procedure for tank testing to Maritime Research Institute Netherlands predict the onset and extent of parametric In addition, the following corresponding rolling. members contributed greatly to the work of the • Further develop the procedure 7.5-02-07- committee: 02.5 for intact stability testing, to include extreme motions such as broaching and • Professor K. J. Spyrou, deck diving in irregular waves, wind and National Technical University of Athens, breaking waves. Liaise with the Ocean Greece Engineering Committee.

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• Identify experimental techniques and data capsize scenarios, and have been used to for validation of time-domain capsize identify different modes of extreme motions codes, emphasising the selection of the and capsizing of intact ships. To perform these important parameters that influence the experiments successfully, the ship model capsizing behaviour of intact and should be self-propelled and fitted with an damaged ships. Liaise with the Ocean auto-pilot to eliminate any external influences Engineering and Seakeeping committees. to the model’s response to the waves. Generally, • Assess the state of the art for: the ship motions should be measured by a o Practical application of numerical fibre-optic gyroscope, a gyro accelerometer or methods for the prediction of capsizing an optical tracking sensor. The measured and experiments for assessment of signals should be stored by an onboard safety/risk against capsize. computer, or transmitted to shore by radio link o Make recommendations as to what or umbilical cable. scientific progress is required to move Roll decay tests and inclining experiments stability regulations from those based should be performed to assess the roll damping on hydrostatic calculations to those and the transverse stability characteristics of based on dynamic predictions, either the model. using capsize codes or physical model Many free-running experiments on experiments. parametric rolling in head and bow seas have • Establish the importance of the following been conducted during the last three years and issues in predicting the dynamic are reviewed in the following section. behaviour of damaged vessels, including Matsuda, et al. (2006) conducted free sinking and capsizing, coupling between running model experiments for a purse-seiner floodwater dynamics and ship dynamics, vessel at several Froude numbers. The model influence of flow coefficients for openings capsized due to bow-diving in the severe and flooding of complex spaces (multiple following seas at intermediate speeds. The compartments, stair wells, failing model also experienced stable surf-riding at watertight doors, etc). higher speeds and broaching at lower speeds. • Review numerical methods for assessing Marón, et al. (2006) and Perez-Rojas, et al. the length of time to sink or capsize for (2007) investigated the accidents of small damaged passenger ships and associated fishing vessels through free running model validation techniques. experiments in beam, following and quartering • Continue to review developments (rele- seas. This allowed the identification of the vant to ITTC) in stability safety assess- modes of loss and the appropriateness of the ment, with special attention on perform- stability regulations for this type of vessel. ance and risk-based approach and relevant developments at IMO. Guided Model Experiments. Captive and semi-captive model experiments can give repeatable and certifiable experimental results 2. PREDICTION OF EXTREME MO- to verify the capability of numerical models, or TIONS AND CAPSIZING OF INTACT to obtain information on forces, moments and SHIPS motions. If the model is towed, the towing point should be carefully selected to avoid undesirable effects on the significant motions. 2.1 Experimental Technique for Capsizing Ikeda, et al. (2005) carried out guided in Wind and Waves model experiments for a large passenger ship to investigate the effects of wave height and Free Running Experiments. Free running bilge keel arrangements on the occurrence of model experiments can be used to investigate parametric roll in beam seas. The model was

Proceedings of 25th ITTC – Volume II 607 equipped with gimbals to keep the model on wave sequence leading to an extreme response course, but was free to heave, pitch, sway and over a short period of time; four approaches roll. Using this model, Munif, et al. (2006) have been identified. The first approach measured ship motions in dead ship conditions adopted is based on linear, broad-banded wave in waves with various heading angles to theory and uses probability theory to find the confirm the region where parametric roll expected value of the wave shape. The second occurred. Fujiwara and Ikeda (2007) also approach uses the Sequential Quadratic Pro- studied the effects of roll damping and heave gramming method to optimize the phases motion on parametric rolling. associated with an initial random wave train, Olivieri, et al. (2006) conducted model such that the result produces the desired experiments in regular beam seas for the extreme waves. The third approach applies the validation of a CFD code. The test conditions first approach described above to find the selected were free to heave and roll, whereas shape of the most likely extreme response, and the other degrees of freedom were constrained. the amplitudes and phases of the incident wave Lee, et al. (2006) observed experimentally the components can then be back-computed via effects of the initial conditions on the linear theory, giving the tailored wave shape capsizing of a box barge in beam seas. The near the desired crest. Alford, et al. (2005, model was fixed at an initial roll angle by 2006) reviewed the approaches described electromagnets, which allowed the model to be above and developed a fourth approach using a released at an expected initial roll velocity. non-uniform distribution for the random Matsuda, et al. (2007) developed a new phases associated with the component waves. measuring system to realize the measurement This method constructs a response time series of heel-induced hydrodynamic forces with using linear superposition of sinusoidal waves deck submergence and forward velocity in with a non-uniform phase distribution to keep following and quartering seas. This system the stochastic nature of the problem. restricts surge, sway, yaw and roll, but allows heave and pitch motions to be free. Wind Generation. For capsize experi- Ayaz, et al. (2006) measured ments at zero speed (drifting), wind forces can 6-degrees–of–freedom (DOF) forces and play an important part as they have a great ef- moments by using a dynamometer in captive fect on ship heading, drifting direction and model experiments, to enhance a numerical heel angle. Experiments with wind effects at manoeuvring model. Lundbäck (2005) and forward speed were not found in current pub- Armaoğlu, et al. (2006) measured the surge lished literature. This is due to fact that the force, sway force, roll moment and yaw profile of the wind velocity is difficult to moment with a 6-DOF loadcell. The models model accurately. were free to move in heave and pitch in their Ogawa, et al. (2006) investigated the experiments. effect of wind and waves on the drift motion through free drifting tests in steady beam wind Wave Generation. Waves used in cap- and irregular beam waves. In the experiment sizing experiments include regular, the wind fans, which are attached to the long-crested irregular, short-crested irregular carriage, track the model as it drifts in the and transient waves. ITTC and JONSWAP waves. The effect of the drift motion on the spectra are usually chosen for the long-crested capsizing probability under dead ship irregular waves. Hashimoto, et al. (2006) used condition was also examined. Umeda, et al. cosine to the 2nd or 4th power as the directional (2006b) carried out a model experiment in a distributions function for generating the towing tank with wind fans to create a beam short-crested irregular waves. wind profile to investigate the capsizing and It is very important for capsizing experi- sinking of a cruising yacht. This experiment ments in transient waves in the basin to tailor a determined the time-to-sink with and without

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608 water inside the yacht. irregular waves (Bulian, et al., 2004; Hash- imoto, et al., 2007). However, even with the elastic mooring line towing arrangement it is 2.2 Experimental Technique for Head-Sea difficult to reproduce speed variation in Parametric Rolling irregular waves, which was noted to have some influence on the probability of A considerable number of model parametric roll (France, et al., 2003). It is experiments investigating head-sea parametric noted that comparative studies between free rolling have been conducted in recent years. running and towed model experiments have They have been carried out not only in regular shown acceptable agreement (SLF waves but also in irregular waves. In the 49/5/7/Corr.1, 2006). However, in order to experiments, wave period, wave height, load take into account the full effect of the vessels condition and speed of the model were varied speed variation in waves, tests with a and their effects on the threshold for the free-running model should be considered. occurrence of parametric rolling and the resultant rolling amplitude were investigated. Non-Ergodicity of Head-sea Parametric Model experiments on head-sea Roll in Irregular Waves. It should be noted parametric rolling are divided into two that there is a possibility of non-ergodicity in categories. The first uses a model towed by a head-sea parametric rolling in irregular waves. carriage or other device in a towing tank Belenky, et al. (2003, 2006) and Bulian, et al. (Burcher, 1990; Silva and Guedes Soares, (2006) carried out numerical simulations of 2000; Francescutto, 2001; Neves, et al., 2002; parametric rolling in irregular waves. Although Bulian, et al., 2004; Hashimoto, et al., 2007). proof of ergodicity or non-ergodicity for The second uses a free-running model with parametric rolling in irregular waves cannot be autopilot in a wide rectangular basin (Dallinga, provided, based on careful analysis of et al., 1998; France, et al., 2003; Matusiak, simulated ship motion data, they concluded 2003; Levadou and van’t Veer, 2006; that roll motion is practically non-ergodic, Hashimoto, et al. 2006; Taguchi, et al. 2006). while pitch and heave motions can be considered as ergodic processes. More recently, Towing Arrangement. For head-sea the possibility of non-ergodicity in head-sea parametric rolling the coupling between roll parametric rolling has been confirmed by and vertical motions plays an important role in model experiment (Bulian, et al., 2004, 2006, addition to the variation of the roll restoring Hashimoto et al, 2007). Bulian, et al. (2008) moment in waves (Skomedal, 1982). Therefore, studied the dispersion in the estimated if a towed model is used, special attention statistical characteristics of the measured should be paid to the towing arrangements to processes in parametric rolling. This study ensure that there is no interference with the showed that the uncertainty in the estimation vertical motions. Burcher (1990), Francescutto from time histories of roll is significantly (2001), and Neves, et al. (2002) described this larger than those for pitch and wave elevation. kind of towing arrangement. For example, In order to consider the possibility of non- Francescutto (2001) used a tethering system ergodicity in parametric rolling, the draft based on pairs of elastic mooring lines revision of the ITTC Recommended Proce- symmetric about the centre line of the model, dures and Guidelines 7.5-02-0704.1 “Model to attach the model to the towing carriage. This Tests on Intact Stability,” recommends that system ensures the model remains on a straight several realisations of irregular waves of course, while it is sufficiently loose to avoid shorter duration be used rather than one any interference with the roll and vertical realisation of longer duration. However, it motions. appears necessary to set up guidelines for the A towed model was used in tests in appropriate run length and number of

Proceedings of 25th ITTC – Volume II 609 realisations required. Therefore, further is also desirable to carry out numerical investigations on this issue from a theoretical, simulations for systematically varied numerical and experimental perspective are conditions and compare both experiments and required. simulations when determining the threshold for the occurrence of parametric rolling and Nonlinear Feature of Head-sea Parametric the resultant rolling amplitude. Rolling Since parametric rolling is a non- linear phenomenon, different steady states could coexist at the same experimental 2.3 Revision of the Model Test Procedure conditions. Oh, et al. (1992, 2000) carried out model The Procedure 7.5-02-07-04.1 “Model Tests experiments in longitudinal regular waves on Intact Stability” has been further developed without forward speed. They continuously based on a survey within ITTC member measured ship motions while varying the wave organizations, on the experiences of experts height by small amounts. The jump-up/down and published literature, to include extreme phenomena were observed and the range of motions such as broaching and bow diving in wave amplitude where two steady states exist irregular waves, transient waves, and in wind. (non-rolling and parametric rolling) was An experimental procedure to examine clarified. parametric roll was incorporated into the Bulian, et al. (2004) reported that two model test procedures. The additions and coexisting steady state roll motions were revisions of the procedure are summarized as observed in regular waves. This was confirmed follows: by Hashimoto, et al. (2007) in regular wave • Regarding the model design and tests at no forward speed with different initial construction, the following important disturbances. To identify the threshold of considerations were added to the original parametric rolling by model experiments, it is procedure: the effects of model hull and therefore necessary to repeat experimental bilge keel sizes on viscous roll damping, runs with the model starting with different turbulence stimulation for rudders and fins, initial conditions (as far as reasonably the projected areas of superstructure for practicable). testing in wind, the significant autopilot Hashimoto, et al. (2006) reported that head contributions to model roll, the towing sea parametric rolling may disappear when the point for towed model, etc. wave height increases in the model experiment. The methods for calibration of the deter- This was noted earlier by several numerical • ministic transient waves at a target area simulation studies by Umeda et al. (2003), were introduced based on members’ Spanos and Papanikolaou (2005), Umeda et al. experiences and a literature review. Two (2005), and Neves and Rodriguez (2005). This options for modelling wind forces were implies that a threshold maximum wave height described: Firstly where wind loads act may also exist for parametric rolling. directly on the model and secondly with a Therefore, it should be noted that the wind velocity field around the model. non-existence of parametric rolling in a certain wave height range does not necessarily mean • The ranges of the ratio of wavelength to that parametric roll will not occur in other ship length for the model experiments in wave height ranges. astern seas and head seas were specified. Taking these nonlinear features of As an interim indication, the generation of head-sea parametric rolling into account, the transient waves was introduced based on revised ITTC Recommended Procedures and relevant literature. Guidelines 7.5-02-07-04.1 “Model Tests on • For a floating structure, wind can be Intact Stability” has been drafted, stating that it generated following the ITTC recom- mended procedures and Guidelines,

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7.5-02-07-03.1 “Floating Offshore Plat- number of experiments examining parametric form Experiments”. For a free drifting rolling in head and bow seas have been model, a wind velocity field may be conducted by universities and research generated by an array of wind fans institutes/laboratories. In order to identify the mounted on a carriage following the suitability of the experimental data for model. validation of numerical benchmark testing, a • Details on roll decay tests were included questionnaire survey was carried out among with regards to the IMO weather criteria the members of this specialist committee and test guidelines published as MSC.1/ some universities. Additionally, a review of Circ.1200 (2006). publications from stability related conferences • Procedures for conducting parametric was made. rolling experiments were described in It was found that some experiments have detail, including theoretical explanations restrictions on the public use of the results, of this phenomenon. especially on the hull form details. Some of the data do not include the necessary details for comparison with simulation results. Three 2.4 Benchmark Testing Plan of Numerical sets of experimental data were selected as Codes for Predicting Parametric candidates for benchmark testing. A summary Rolling of the data is indicated in Table 2.1.

Benchmark Testing in 23rd and 24th ITTC. Table 2.1 Summary of Identified Data To establish the capability and weaknesses of Data Name ABC Post Panamax ITTC time-domain numerical capsize codes on intact Panamax Ship type container A-1 container stability, benchmark studies were conducted in (4000TEU) container (C11-class) the 23rd ITTC (The Specialist Committee on Length(Lpp) [m] 262.0 260.0 150.0 Prediction of Extreme Ship Motions and Breadth [m] 40.0 32.2 27.2 Depth [m] 24.5 20.0 13.5 Capsizing) and the 24th ITTC (The Specialist Mean draught [m] 12.9 12.0 8.5 Committee on Stability in Waves). Block coefficient 0.593 0.640 0.667 GM [m] 1.97 1.12 1.00 In the 23rd ITTC, free-running test data of Natural roll period [sec] 25.7 26.4 20.1 a container ship (Ship A-1) and a purse-seiner Model scale ratio 1/55 1/100 1/60 Type of test Free running (Ship A-2) in following and quartering seas Froude number 0.11-0.22 0.0-0.25 0.0-0.25 were used for validation. The capsize modes Encounter angle [deg] 120-180 180 180 regular Wave / ship length 1.2 0.6-2.4 0.8-1.25 were mainly parametric rolling at low speeds wave Wave steepness 0.015 0.008-0.046 0.03-0.05 for the container ship and broaching in high irregular T02 [sec] 13.6-16.2 wave H1/3 [m] 11-13 speed conditions for the purse-seiner. France et Yang et al. Umeda Key Reference The same purse-seiner used in the 23rd al. (2003) (2008) (2007) ITTC (Ship A-2) was used in the 24th ITTC validation study. These validation tests includ- From this data set, Data-C is the first ed data from roll decay tests, free running tests candidate for head-sea parametric rolling. The in beam and quartering seas and captive tests hull form of Data-C, used in the 23rd ITTC, is for measuring GZ variation in waves. As in the not of a modern container ship. However, the 23rd ITTC, the main capsize mode was measured roll restoring variation in waves, broaching in following and quartering seas. wave-induced surge force data and others are Considering the activities of the current available from captive model experiment and previous specialist committees, emphasis results. should be placed on examining parametric The Data-A can be used as validation data rolling in head and bow seas in the next for bow-sea parametric rolling, especially in benchmark testing study. irregular waves, though captive model experiments were not conducted. Identification of Data. A considerable

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stability conditions often leading to capsize and sinking. The international scientific Plan for Benchmarking. In the 24th community has further developed and ITTC, a benchmark study for broaching was improved numerical methods to match the carried out step by step as follows: findings from physical model experiments. 1) Dynamic behaviour in still water (roll decay and basic manoeuvrability); 2) Roll and sway responses in beam seas; 3.1 Numerical Simulation Modelling and 3) Roll, sway, yaw and surge responses in Techniques quartering seas; 4) Magnitudes of hydrodynamic loads asso- The numerical methods for the simulation ciated with the above. of the motions of a damaged ship in waves can In the new benchmark study, similar steps be categorized according to the modelling and would be effective for establishing the integration of the basic three constituents of capability and weaknesses of the codes: the problem which are employed, which are: 1) Roll decay test as a function of forward • The ship with zero forward speed drifting speed; on the free surface under the excitation of 2) Roll, and pitch responses in head seas; waves; 3) Hydrodynamic forces and moments in • The behaviour of the accumulated flood- waves water inside the ship’s compartments and its interaction with the ship; When using Data-C for validation, the • The flooding phenomenon itself, namely three steps described immediately above are the process of water inflow and outflow possible, and the important factor, the roll through the damage openings and the restoring variation in head waves, can be progressive flooding through internal compared with experimental data. spaces. The benchmark study can be divided into two phases. In the first phase, all of the As a basis of most numerical methods, hydrostatic and hydrodynamic quantities will potential flow theory is commonly employed be estimated by the benchmark code from the to address ship-wave interaction and is adapted hull form, shape of bilge-keels details, etc. In to account for large amplitude motions and the second phase, the numerical simulation supplemented with empirical models for will be conducted using all of the measured viscous effects. The influence of the damage data. Comparing the results of the two phases opening on the wave forces is generally will allow the capabilities and weaknesses of neglected. the codes to be identified. The hydrodynamic properties of the When Data-A is used, step 3 above will not damaged ship are commonly calculated in the be possible. However, comparing the results frequency domain and transferred to the time from steps 1 and 2 would allow the domain by means of retardation functions used characteristics of the codes to be understood. in the memory effect integrals. The slow change of hydrodynamic properties as the floodwater accumulates inside the ship and 3. PREDICTION OF DYNAMICS OF changes the mean draft and trim, can be DAMAGED SHIPS addressed by an appropriate update of the ship’s hydrodynamic coefficients. The effect of the mean heel angles on hydrodynamic Research has progressed in recent years in coefficients is generally ignored. the area of numerical prediction of the motions The modelling of the floodwater inside the of a damaged ship in waves with marginal damaged compartments is a challenge for all

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612 numerical methods. There are different theoretical and experimental prediction of approaches used to address the floodwater damaged ship stability in waves are the series dynamics and the effects on the ship motions. of STAB Conferences (eg. STAB, 2006) and The accuracy and efficiency of the model is ISSW Workshops (eg. ISSW 2005, 2007). dependent on the underlying methods used. Higher accuracy CFD methods are currently Flooding Process. Katayama and Ikeda not yet practical for full integration with ship (2005) carried out physical model tests and motion simulation methods for multi- documented the dependence of the discharge compartment configurations. The commonly coefficients on the basic geometric parameters used simpler quasi-steady approaches can of the damage opening, as well as the result in unsatisfactory results, for instance in ventilation conditions of the damage cases with large deck areas, when sloshing compartment. The assumption of a constant effects are significant. There is also uncer- value of the discharge coefficients appears to tainty on the correct values for the discharge be a special case within the wide variety of coefficients, which relate the pressure differ- discharge conditions that can be encountered. ence over an opening to the resulting flow Cho, et al. (2006) applied a 2-D analytical velocity through the opening. CFD method to the floodwater sloshing The possible use of shallow water problem, which interacts with the motions of equations for the flooding problem is limited the damaged ship. The preliminary results by the difficulties which occur with the partial presented could not demonstrate any improve- emergence of the bottom of the flooded ment of the simulated motions of the damaged compartment, a phenomenon which is almost ship; however, there is evidence of an always present, at least over a portion of the improvement of the computational perform- simulation time. The use of the random choice ance of the overall method that supports the method or Glimm’s method (Santos and feasibility of such refined numerical methods Guedes Soares, 2006) overcomes the bottom for the analysis of at least more intricate emergence difficulty, where an approximate flooding cases. solution for the time-domain flow of Ruponen (2006a) presents a new floodwater can be obtained. simulation method for progressive flooding of The use of particle methods has damaged ships. The method is based on the demonstrated the ability to model complicated so-called pressure correction technique to deal phenomena like wave breaking and sloshing with the coupled water and air flows. Water behaviour. The main disadvantage of these and air flows have very different densities and emerging methods is their heavy pressures which leads to numerical difficulties computational requirement, which currently in ordinary time integration schemes. The makes it difficult to integrate with ship motion iterative structure of Ruponen's method simulations. ensures time accurate results for complex An effect of the flooding process that also compartment configurations. Ruponen also needs to be accurately modelled is that of compares simulation results with experimental trapped air in cases with unventilated or results and finds a very good agreement in partially ventilated compartments. Trapped air calm water flooding. will have a significant influence on the water Nabavi, et al. (2006) studied the effect of accumulation in compartments. geometrical parameters of openings on the discharge rate for water flowing off a deck. The study was based on CFD simulations and 3.2 Recent Literature the results were compared to experimental data. The results show that the propagation of The two main sources of information on longitudinal waves causes the discharge the developments and achievements in the coefficient to fluctuate. Furthermore, results

Proceedings of 25th ITTC – Volume II 613 from two-dimensional simulations were in considers the equations of motion in the time close agreement with these from domain and describes the behaviour of the three-dimensional simulations. floodwater inside the ship’s compartments Skaar, et al. (2006) demonstrates the using shallow water equations. Differential applicability of SPH techniques to model equations describing the properties of the progressive flooding of a damaged ship section. water on the main deck are also given. A The section was forced to oscillate in roll and number of damage conditions are studied for heave. Despite a number of known difficulties the flooding of a double bottom and main pertinent to SPH methods (wave generation, compartments without water on the main deck. wave reflection, numerical dissipation, wall Comparisons with experimental results for a boundaries), the ability to capture the flooding Ro-Pax ferry are discussed. process with subsequent internal sloshing was For intact conditions, the calculated and demonstrated. experimental roll characteristics were found to Ruponen (2007) discusses improvements be in good agreement. For flooded conditions and advances to his simulation method for the agreement was less satisfactory. progressive flooding. In particular, the way to Nevertheless, a double peaked roll response deal with openings which have a large vertical spectrum found in the experiments could be extent and a sensitivity analysis of the reproduced with the numerical method. developed method with respect to opening Cho, et al. (2006) present a numerical parameters are discussed. method to solve ship motions with internal It is found that the failure of (semi) water fluid. The ship motions problem is solved tight doors is rather sensitive to initial leakage using a three-dimensional frequency domain which reduced the pressure differences over panel method. The internal water motion is the doors. It is concluded that the failure based on a VOF method modified to take processes should be more closely studied. On account of sloshing effects. The ship and the the other hand, the sensitivity analysis did not internal water motions are coupled by adding show significant differences in the overall sloshing forces to the ships equations of flooding process due to small variations to motion. In turn, the ship motions affect the critical pressure heads. sloshing of the internal water. Comparisons Ruponen and Routi (2007) describe a with experimental results for a Ro-Pax vessel method for the dimensioning of air pipes on show that for resonant roll conditions, a good the basis of his flooding simulation method. agreement is found for the roll decay The method is applied for the calculation of properties. For non-resonant conditions the the time to cross-flood in a U-shaped void agreement is not so good. (double hull) of a large passenger ship. Air Spanos and Papanikolaou (2007) have compressibility is accounted for in the method. analysed the time to capsize of a damaged Ro-Pax ship in waves by means of a numerical

simulation procedure. The procedure consists Numerical Simulations for Damaged of a non-linear hydrodynamic method for the Ships. Worldwide, the number of researchers simulation of the ship motions and flooding, dealing with the development of numerical with a statistical simulation method to account simulation tools appropriate for the assessment for the variability and uncertainty of the of the damaged ship stability in waves appears various parameters involved. to be increasing. Recently introduced The hydrodynamic method consists of a simulation methods/codes previously unknown non-linear time domain simulation method in were those of Schreuder (2005), Jankowski six degrees of freedom. The motion problem is and Laskowski (2006). based on linear potential flow theory in Santos and Guedes Soares (2006) describe combination with non-linear Froude-Krylov a numerical method for the motions of a forces. The flooding problem is based on a damaged ship in a seaway. The method

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614 quasi-steady approach using the Bernoulli SAFEDOR (2005-2008); this study was equation. supported by the 25th ITTC Specialist The statistical method is based on the Committee SiW and coordinated by the Monte Carlo approach in which the numerical National Technical University of Athens method is applied for a series of randomly NTUA. chosen conditions. Benchmark codes have been reviewed in a It is shown that there is no practical time comparative way with respect to the prediction margin for the evacuation of passengers and of the survival boundary of a damaged Ro-Pax crew in non-survival conditions. The results ferry in waves, as well as with respect to the also suggest that the ship, which complies with sensitivity of the numerical predictions on the current damage stability requirements, will basic simulation parameters of inherent always capsize in waves exceeding a limiting uncertainty. (survival) wave height. This benchmark is considered as a Walree and de Kat (2006) have applied continuation of the two earlier benchmarks their time domain simulation method to studies conducted for the 23rd and 24th ITTC. forensic research on the loss of a trawler and Although six (6) institutes initially expressed a analyzed the survivability of the vessel in view formal interest in participating in the study, of deck flooding and down-flooding through eventually only the results from four (4) of open hatch covers. them were available in a timely manner and Vassalos and Jasionowski (2007) have used in related comparisons, Table 3.1. The examined a series of related numerical low participation provides evidence that there simulations and relevant experimental results are only a limited number of independently for a Ro-Pax and cruise ship. They developed and mature codes available world- highlighted issues with the new harmonized wide for analysing this very complicated and probabilistic rules SOLAS2009 for these important issue. vessels types. Valanto (2007) has applied a numerical Table 3.1 List of Final Participants simulation code for the re-investigation of the Institute/ Acronym Country Estonia ferry accident; possible scenarios of organization sinking were deduced by analysis of National Technical NTUA-SDL Greece simulations for the possible flooding of the car University of Athens – deck. Parallel forensic investigations by other Ship Design simulation codes on the same subject were Laboratory discussed during the international workshop The Ship Stability SSRC United on the Estonia ferry accident (Estonia Debate, Research Centre, Kingdom Universities of 2007). Glasgow and Strathclyde Maritime Research MARIN The 3.3 Benchmark Testing of Numerical Institute Netherlands Netherlands Modelling Instituto Superior IST Portugal Tecnico, Since 2001, numerical simulation codes Technical University of appropriate for the assessment of the Lisbon survivability of a damaged ship in waves were monitored and have been benchmarked by the 23rd and 24th ITTC. For the assessment of the The Study Ship. The vessel used in the current performance of related codes, an investigation is a modern Ro-Pax ferry with a international benchmark study was organized bulbous bow and flat stern sections. The main within the European research project dimensions of the ferry are given in Table 3.2

Proceedings of 25th ITTC – Volume II 615 and the body plan is shown in Figure 3.1. The remains intact after the damage. ship is of SOLAS 90 stability standard and has Benchmark Tests. The ferry is assumed been investigated previously within the to be free floating, without forward speed, in European research project HARDER (2000 beam waves coming from the starboard side, -2003). Two bilge keels of 0.34m width are the side that is damaged, and is free to drift. fitted on the hull; the astern one has a length of As listed in Table 3.3, the benchmark tests 23.6m and the forward one a length of 28.0m. consisted of the estimation of the survival

boundary Hs,surv for a set of five different Table 3.2 Main Dimensions of the Study Ship conditions and an additional seakeeping test. Length Lpp 174.80 m All the tests were for the SOLAS damage case described above. Tests 2 to 5 were for the Beam, B 25.00 m same conditions, as in Test 1, but had certain Draft, T 6.40 m parameters varied as a sensitivity investigation. Depth, D 9.10 m Hence, in Test 2 the KG was reduced by 1.0 m, in Test 3 longer period waves were considered, in Test 4 any assumption on the semi-empirical The Damage Case. The damage case value of the roll viscous damping that was investigated includes damage to two adjacent made for the initial test was doubled, and in compartments located amidships and corre- Test 5 the assumed discharge coefficients for sponds to the worst SOLAS 90 damage case. the initial test was reduced by half. The last The length of the damage opening is 8.25m test conducted, Test 6, was a seakeeping test in (3%L+3.00 m), with a triangular penetration which the vessel started in the intact condition and unlimited vertical extent including damage and after 30 minutes the damage (the same as to the vehicle space on the main deck. The for the other tests) was assumed to occur. general arrangement of the damaged compart- ments is shown in Figure 3.2.

2.5 2.5

2.0 2.0

1.5 MAIN DECK 1.5

Engine Blocks z/T

1.0 1.0

0.5 0.5 E.R. Double Bottom

0.0 0.0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 y/B Figure 3.1 The Body Plan of the Study Ship

In the engine room (the aft damaged compartment) two intact blocks are used to model the main engines and result in an engine room permeability of 0.70. In the double bottom of the fore compartment the two side tanks are interconnected with a cross duct, Figure 3.2 General Arrangement of the while the rest of the space between them

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Damage Case Investigated P4 3.00 +0.00

Table 3.3 Benchmark Tests (with respect to the It should be noted that insufficient model Particulars of Tests 2–5 only the differences tests were actually conducted to establish an relative to Test 1 are given) experimentally measured survival boundary for the benchmark; the tests conducted showed, Test Description Particulars however, that the actual survival boundary was 1 Basic KG = 12.3 m, close to, but less than, 3.00 m. JONSWAP, Two of the simulation codes successfully p = 4 HsT , γ = 3.3, predicted a survival boundary with a wave B44v-basic , Cdischarge-basic height of about 3.00 m, while significant 2 Low KG KG=11.3 m 3 Long waves deviations of 1.0 m were detected for the other p = 6 HsT , γ = 1.0 two codes. Detailed background investigation 4 High roll viscous B44v΄ = 2 x B44v-basic on the two successful codes P1 and P4 damping revealed, however, that they substantially 5 Reduced discharge C΄ = 0.5 x discharge differed in intermediate results during the coefficients Cdischarge-basic 6 Seakeeping KG = 11.3 m, Hs = study, though this is not reflected in the final 3.0 m, estimated survival wave height of the Tp = 10.4 sec, γ =1.0, benchmarked ship. B44v-basic , The sensitivity of the numerical Cdischarge-basic, Damage onset after 30 predictions with respect to the basic simulation min parameters, namely those of the ship loading condition KG, the spectral sea wave periods, the roll viscous damping and the discharge Survival Boundary Estimations. The coefficients were examined with an additional study participants were required to deliver series of tests. The numerical results, their best prediction for the specified summarized in the Table 3.5, show that the conditions, considering any assumptions made codes exhibited different sensitivities and and semi-empirical data used, and the applica- predicted opposite trends in certain cases, with tion of the code as inherent to the bench- respect to the basic variations. marked method. Comparable conditions were assumed to be established when the intact ship Table 3.5 Difference of Survival Boundary in hydrostatics and the basic benchmark Comparison to the Basic Test 1 specifications were met by the benchmarked Participant Test 2 Test 3 Test 4 Test 5 codes. Special care was taken to ensure the Lower Longer Higher Lower reliability of the delivered numerical results in (by Waves (double) (half) view of the probabilistic nature of the problem. 1.0 m) Roll discharge The delivered numerical simulation results KG Damp. coefficients for the survival wave heights are shown in P1 0.40 0.31 0.02 0.57 Table 3.4, where the names of participants are coded as P1 to P4 and kept anonymous. P2 0.50 1.25 0.00 -0.25 P3 0.75 -0.50 0.00 0.00 Table 3.4 Survival Boundary in (m) for the P4 0.50 -0.75 N/A N/A Basic Test 1 The numerical estimations of survivability Participant Hs,surv Mean Differ. from Exp. mean of the benchmarked ship were most sensitive to the ship loading condition and the spectral P1 3.23 3.00 +0.23 ≤ periods of the incident waves, while less P2 1.75 -1.25 3.00 sensitive to the assumptions made for the P3 4.00 +1.00 discharge coefficients. No conclusions could

Proceedings of 25th ITTC – Volume II 617 be derived for the effect of the viscous roll complex scenarios. damping as the present results appear to The initial intention was to carry out a contradict the conclusions from the earlier benchmark study for an existing cruise ship. benchmark studies, suggesting an increased Unfortunately, the data for a realistic cruise importance for the values of the ship with a complex internal geometry were semi-empirical roll damping coefficients. not readily available to the Committee. Independent of the successful prediction of Therefore it was decided to split the work in the survival wave height boundary by two two phases as follows: codes, the rating of the overall performance of 1. A benchmark based on a barge for the benchmarked codes could not be which detailed model test data is available; concluded, as verification of the reasons for 2. A benchmark based on a realistic the inferior performance of the other codes is passenger ship with complex internal still pending. geometry. Further details and background informa- tion about the benchmark study, its conditions and activities can be found in Papanikolaou Benchmark Study Phase 1. The and Spanos (2008), as well as on the webpage objective of the benchmark study was to www.naval.ntua.gr/~sdl/sibs. The final results establish the current capabilities and of this study would be reported by SAFEDOR weaknesses in predicting, qualitatively and in a forthcoming IMO-SLF paper. quantitatively, the time-to-flood for a simple configuration of compartments in a barge-like hull form. Besides time-to-flood, related 3.4 Benchmark Testing of Numerical Codes quantities such as motions and flooding of Time-to-Flood volumes in compartments were compared with experimental results. Introduction. The ITTC Stability in The barge that was used as the basis for Waves committee has conducted two the study has been tested at the Helsinki benchmark studies on numerical methods for University of Technology (TKK, formerly the prediction of time to flood of damaged HUT), see Ruponen (2006b). The model was ships in a seaway. Both studies were box shaped with tapered bow, stern and bilges. completed under the coordination of the 25th The model scale was 1:10 with a model length ITTC committee and were performed at the of 4 m, see Table 3.6 and Figures 3.3–3.5. The request of the SLF Sub-Committee of the IMO. model was instrumented with water level The studies have contributed to the assessment sensors in the eight floodable compartments to of the state of the art of numerical methods. obtain detailed information on the flooding Results of the studies have been and will be process. Two pressure sensors were located in reported at the 50th and 51st sessions of the the two lower, double bottom compartments. SLF Sub-Committee (Walree 2007: Walree The floodable compartments were located and Carette, 2008a). Furthermore, results have forward of amidships so as to introduce a trim been presented at the ISSW 2007 and 2008 angle and thereby encourage progressive workshops, see Walree and Papanikolaou flooding. (2007) and Walree and Carette (2008b). The development of a structured approach Table 3.6 Main Particulars of Barge Model to benchmark testing was a key feature in the Length over all 4.000 m benchmarking process. Several comparisons of predictions for the time-to-flood and motions Breadth 0.800 m in calm water and in waves, obtained from Height 0.800 m running the participating numerical codes, Design draft 0.500 m have been reported for progressively more

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Block coefficient 0.906 Volume 1.450 m3 The following organizations participated in Phase 1 of the benchmark study: Six flooding cases were tested in the experiment, four of which were selected for 1. Ship Stability Research Centre (SSRC), the benchmarking study. The experimentally United Kingdom. derived discharge coefficients were used in the 2. Helsinki University of Technology (TKK), simulations. The details of the experimental Finland. configurations are described by Ruponen 3. Maritime Research Institute Netherlands (2006b). (MARIN), The Netherlands. 4. Maritime and Ocean Engineering Research Institute (MOERI), Korea 5. National Technical University of Athens (NTUA), Greece. In the presentation of the results the participants are referenced to anonymously as C1 to C5. All of the codes tested incorporate time domain simulation methodologies and can predict ship motions in six degrees of freedom. Figure 3.3 Barge Model at TKK The codes are applied for conventional ship hulls at zero or normal operating speeds.

Froude-Krylov forces are based on the integration of the undisturbed wave pressures over the instantaneously submerged hull and superstructure portions. Radiation and diffrac- tion forces are generally based on strip theory or a 3D frequency domain panel method. This frequency domain information is used in the time domain by means of convolution integrals. The hydrodynamic force components that are influenced significantly by viscosity are modelled semi-empirically. The flooding methods use relatively simple hydraulic models. The basic Bernoulli equation is used to determine the water ingress through damage openings. The flow rate through an opening is related to a pressure Figure 3.4 Barge Configuration difference over the opening and a semi-empirical discharge coefficient. This approach is also applied to the progressive flooding between ship compartments through open doors, ducts, collapsed bulkheads, etc. None of the codes take into account sloshing effects. The water surface in compartments is either assumed to be horizontal at all times, or a local gravity angle is applied such that the water surface is still planer but not necessarily Figure 3.5 Internal Compartments horizontal.

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Plots showing comparisons between the show good comparison. experimental (Test) and simulation results (C1 through C5) are shown in Figures 3.6 through H-DB1 Test 03 3.16 (Test 03). Water level heights in the 1.8000E+02 compartments are denoted by H-x where x 1.6000E+02 1.4000E+02 stands for the compartment identification. The 1.2000E+02 Test C1 pressure in the double bottom compartment 1.0000E+02 C2

8.0000E+01 C3 H [mm] DB1 is denoted by P-DB1. Sinkage and trim C4 are denoted by heave and pitch, respectively. 6.0000E+01 C5 4.0000E+01

Water level results from Code C1 are only 2.0000E+01 defined between the instants that the level 0.0000E+00 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02 7.0E+02 starts to rise and that the compartment is filled. Time [sec]

Otherwise a zero value is given. Figure 3.6 Water Level for Compartment DB1 In Code C2 a very low atmospheric pressure is present and so this method cannot be applied correctly at model scale. The ambient air pressure is fixed in the code and H-DB2 Test 03 cannot be changed and therefore the effects of 1.8000E+02 air compressibility are likely to be 1.6000E+02 underestimated. 1.4000E+02 1.2000E+02 Test The results for Codes C3 and C4 do not 1.0000E+02 C1 C2 8.0000E+01 include pressures, as air compressibility is not C3 H [mm] 6.0000E+01 C4 taken into account in the simulations. The C5 4.0000E+01 compartments are assumed to be fully 2.0000E+01 ventilated. 0.0000E+00 0.0E+00 5.0E+01 1.0E+02 1.5E+02 2.0E+02 2.5E+02 3.0E+02 -2.0000E+01 The results for the individual compart- Time [sec] ments for Code C5 have been grouped into larger compartments: DB1+DB2 and R21+ Figure 3.7 Water Level for Compartment DB2 R21S+R21P. Results for grouped compart- ments cannot be compared directly to the results for the individual compartments. In some of the codes it was possible to use H-R11 Test 03 the experimentally determined discharge 5.0000E+02 coefficients; in other codes a fixed discharge 4.0000E+02 coefficient has been used. 3.0000E+02 Test C1 C2 The external damage opening for this test 2.0000E+02 C3 H [mm] case was present in the bottom of compartment C4 DB2 and allowed to progressively flood into 1.0000E+02 C5

0.0000E+00 the other compartments. Compartment DB1 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02 7.0E+02 was not ventilated; all other compartments -1.0000E+02 Time [sec] were ventilated to some extent. For the non-ventilated compartment DB1, Figure 3.8 Water Level for Compartment R11 the results show that Code C1 overestimates the air pressure effects, C3 and C4 do not account for air pressure while the Code C2 result is closest to the experimental flooding For the R11, R21, R21S and R21P rate. For the ventilated compartment DB2, the compartments located on top of the double agreement is better. Code C3 results lag behind bottom, the Code C1 result is very close to the the experiment result, but Code C4 results experiment result, C2 shows a flooding rate

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that is too high while C3, C4 and C5 lag H-R21S Test 03 behind the experiment result. 5.0000E+02

For the top compartments R12 and R22, 4.0000E+02 Code C2 results show flooding too early 3.0000E+02 Test compared to the experiment result, C1 and C3 C1 C2 2.0000E+02 C3

results are close to the experimental values. H [mm] C4 Code C4 predicts no flooding in these 1.0000E+02 C5

compartments. C5 lags behind for R12 and 0.0000E+00 R22. 0.0E+00 5.0E+01 1.0E+02 1.5E+02 2.0E+02 2.5E+02 3.0E+02 -1.0000E+02 The pressures in compartment DB1 are Time [sec] well predicted by Code C1, while C2 shows Figure 3.10 Water Level for Compartment again a steeper pressure rise than measured in R21S the experiment. The results for the water level comparison are also reflected in the heave and pitch curves: the heave and pitch rates for C2 are too high but the steady values are well predicted. H-R21P Test 03 Code C1 results are close to the experimental 5.0000E+02 values while C3 results also show high heave 4.0000E+02 and pitch rates and somewhat high steady 3.0000E+02 Test C1 values. This is a contradiction to the general C2 2.0000E+02 C3 H [mm] under prediction of the flooding rates for C3. C4 For Code C4, both heave and pitch are under 1.0000E+02 C5 predicted, which is in agreement with the 0.0000E+00 general under prediction of flooding rates. 0.0E+00 5.0E+01 1.0E+02 1.5E+02 2.0E+02 2.5E+02 3.0E+02 -1.0000E+02 Time [sec] Code C5 finally predicts the heave quite well while the pitch is slightly underestimated. Figure 3.11 Water Level for Compartment In conclusion, the prediction of flooding R21P rates, especially for unventilated or partially ventilated compartments shows large variations. Differences are found between experimental and simulation results and H-R12 Test 03 between the results from the different 7.0000E+02 simulations. Code C1 performed generally 6.0000E+02 well throughout. 5.0000E+02 Test 4.0000E+02 C1 C2 3.0000E+02 C3 H [mm] C4 H-R21 Test 03 2.0000E+02 C5

5.0000E+02 1.0000E+02

0.0000E+00 4.0000E+02 0.0E+00 5.0E+01 1.0E+02 1.5E+02 2.0E+02 2.5E+02 3.0E+02 3.5E+02 4.0E+02 4.5E+02 5.0E+02

-1.0000E+02 3.0000E+02 Test Time [sec] C1 C2 2.0000E+02 C3 Figure 3.12 Water Level for Compartment H [mm] C4 1.0000E+02 C5 R12

0.0000E+00 0.0E+00 5.0E+01 1.0E+02 1.5E+02 2.0E+02 2.5E+02 3.0E+02 3.5E+02 4.0E+02

-1.0000E+02 Time [sec] Figure 3.9 Water Level for Compartment R21

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H-R22 Test 03 As such, reasonable time to sink

7.0000E+02 predictions appear feasible by most of the 6.0000E+02 present codes, at least for ships having a 5.0000E+02 relatively simple internal geometry and Test 4.0000E+02 C1 interconnection between flooded compart- C2 3.0000E+02 C3

H [mm] ments under calm water conditions. C4 2.0000E+02 C5 1.0000E+02

0.0000E+00 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02

-1.0000E+02 Pitch Test 03 Time [sec] 2.0000E+00 Figure 3.13 Water Level for Compartment 1.8000E+00 1.6000E+00

R22 1.4000E+00 Test 1.2000E+00 C1 C2 1.0000E+00 C3

Pitch [deg] 8.0000E-01 C4

6.0000E-01 C5

P-DB1 Test 03 4.0000E-01

6.0000E+03 2.0000E-01

0.0000E+00 5.0000E+03 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02 7.0E+02 Time [sec] 4.0000E+03

3.0000E+03 Test Figure 3.16 Pitch of the Barge C1 P [Pa] 2.0000E+03 C2

1.0000E+03

0.0000E+00 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02 7.0E+02 Comparative Study Phase 2. The objective -1.0000E+03 of Phase 2 of the study was to establish the Time [sec] current capability and weaknesses in predicting, Figure 3.14 Pressure for compartment DB1 qualitatively and quantitatively, the time-to- flood for complex configuration of com- partments in a typical passenger ship. The study was limited to a comparative study of Heave Test 03 numerical results since there currently is no

0.0000E+00 0.0E+00 1.0E+02 2.0E+02 3.0E+02 4.0E+02 5.0E+02 6.0E+02 7.0E+02 8.0E+02 9.0E+02 1.0E+03 public domain experimental data available to -1.0000E+01

-2.0000E+01 conduct a true benchmark study. Besides

-3.0000E+01 Test time-to-flood, related quantities such as ship -4.0000E+01 C1 C2 motions and flood water masses in com- -5.0000E+01 C3 -6.0000E+01 C4 partments were compared. Due to the Heave [mm] Heave C5 -7.0000E+01 complexity of the simulations required and the -8.0000E+01 restricted time constraints, only two partici- -9.0000E+01 pants completed this study. -1.0000E+02 Time [sec]

Figure 3.15 Heave of the Barge Table 3.7 Main Ship Particulars Mass 56542 [ton] Lpp 247.7 [m]

B 35.5 [m] At the same time, differences in local T 8.3 [m] flooding rates on the total flood water mass GM 2.0 [m] apparently cancel out, since the equilibrium position is reasonably well predicted by most The hull form and the internal com- codes. partment layout used here were kindly

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622 provided by SSRC, see Table 3.7 and Figures extended across two compartments. Discharge 3.17 and 3.18. The only appendages present coefficients were determined by each partici- were a set of bilge keels with length 75 m and pant. height 0.5 m.

Figure 3.17 Passenger Ship Compartments

In total 142 compartments were present with 84 openings in horizontal and vertical direction. Most of the compartments were subject to flooding. The ship was freely drifting (zero initial forward speed) for all simulations. No wind forces were taken into account. All six modes of motion were free, i.e. no mode was restricted. The initial position of the ship was Figure 3.18 Passenger Ship Openings such that the wave direction was on the starboard side of the ship (90 deg from stern), i.e. the damage faced the incident waves. The following Simulations were requested The damage length was set as for the Intact Vessel: 0.03*Lpp+3m. The damage height equalled the depth of the ship while the damage depth ° Four sea states, long-crested seas was B/5. ° Ten wave seeds (wave realizations). ° Simulation duration 1800 sec. The shape of the damage was triangular in ° One loading condition. top view, pointing into the ship with depth B/5. Two damage positions were chosen; The following were done for the Damaged Vessel: D1: centre at frame 100 (aft of midship) D2: centre at frame 180 (midship). ° Two damage positions, D1 and D2. ° Five sea states. Both damage positions were at the star- ° Ten wave seeds (wave realizations). board side of the ship. The damage length was

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° Simulation duration until mean heel angle into account. is constant but at least 1800 sec. Preliminary results were published by ° One loading condition. Walree and Carette (2008b). A selection of ° Additional calm water runs. time to flood results is presented as obtained ° Additional runs with fixed heading angle from code B. and specified discharge coefficient. Following the ITTC recommended procedure for damage stability in waves, the The following organisations participated survival limit of the ship is defined as either an in phase II of the benchmark study: instantaneous roll angle of 30 degrees or a ° Ship Stability Research Centre (SSRC), three minute average roll angle of 20 degrees. United Kingdom On reviewing the results for Code B, the ° Maritime Research Institute Netherlands roll and damage mass are not always constant (MARIN), The Netherlands near the 1800 seconds limit and the criteria can In the presentation of the numerical be exceeded during longer duration simulation results, the participants are simulations, especially for aft damage case D1. referenced anonymously as A and B. Typical examples are shown in Figures Both codes incorporate time domain 3.19–3.22. In each Figure, results are shown simulation methods and can predict motions in for five wave realisations. Figures 3.19 and six degrees of freedom. The codes are applied 3.20 show the three minutes average heel to mono-hulls at zero for normal operating angles versus time, while Figures 3.21 and speeds. Froude-Krylov and restoring forces are 3.22 show the three minute average flood based on the integration of the undisturbed water mass versus time. wave pressures over the instantaneously It can be seen that for damage case D1 (aft submerged hull and superstructure. Radiation damage) and Hs = 4m significant wave height, and diffraction forces are generally based on the survival limit is reached in about 2500 to strip theory or a 3D frequency domain panel 3000 seconds. Damage case D2 (mid ship method. This frequency domain information is damage) is less critical in these conditions. used in the time domain by means of On reviewing the preliminary results from convolution integrals (retardation forces). The Code A, they show that the three minute hydrodynamic force components that are averaged values for roll and damage mass are influenced significantly by viscosity are constant near the 1800 second simulation generally determined semi-empirically. Part of duration. Therefore, Code A simulations stop the second order wave drift forces are included here and the criteria are never exceeded. At the by determining the non-linear Froude-Krylov time of reporting the results were still under forces. investigation to determine the significant The flooding methods use relatively differences between the results from the two simple hydraulic models. A modified Bernoulli codes. equation is used to determine the water ingress Based on a preliminary analysis of results, through damage openings. The flow rate it is concluded that for the most severe through an opening is related to a pressure flooding and sea conditions there were head and a semi-empirical discharge considerable differences in the results from the coefficient. This approach is also applied to two codes for the time to flood for a large the progressive flooding between ship passenger ship with complex interior layout. compartments through open doors, ducts, The true performance of the current codes can collapsed bulkheads, etc. The flooded only be evaluated when accurate experimental compartment water surface is either assumed model benchmark data are available for to be horizontal at all times, or movable due to comparison. the coupling with the ship motion, but still planer. Air compressibility effects can be taken

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30 8000 20 7000 6000 10 5000 0 4000 M [ton]

Roll [deg] Roll -10 3000 2000 -20 1000 -30 0 0 1000 2000 3000 0 1000 2000 3000 Time [sec] Time [sec]

Figure 3.19 Roll Versus Time, Hs = 4 m, Figure 3.22 Flood Water Mass Versus Time, Damage Case D1 Hs = 4 m, Damage Case D2

3 4. STABILITY SAFETY ASSESSMENT 2 1 0 In this chapter, only current work on intact -1 stability safety assessment is reviewed, Heel [deg] Heel -2 because mainly performance-based approaches -3 to intact stability are discussed during this -4 term at the navies and IMO. 0 1000 2000 3000 Time [sec]

Figure 3.20 Roll Versus Time, Hs = 4 m, 4.1 Review of Techniques for Naval Ships Damage Case D2 Existing Naval Stability Standards. With

few exceptions, the navies of the world are

still employing hydrostatic based stability 20000 criteria that reflect growths or extensions of the works of Rahola (1939) and Sarchin and 15000 Goldberg (1962). Although static based criteria are currently used there is recognition of the 10000 need to further develop the stability criteria to M [ton]

5000 incorporate hydrodynamics and performance based approaches. 0 There have been a number of recent papers 0 1000 2000 3000 and reports relating to the subject of dynamic Time [sec] stability assessment for naval vessels, cf. Alman, et al. (1999), McTaggart (2000), Figure 3.21 Flood Water Mass Versus Time, McTaggart and de Kat (2000), and Hughes Hs = 4 m, Damage Case D1 (2006). Many of these have been motivated by the work of the Naval Stability Standards Working Group (NSSWG) a collaborative effort between the Royal Australian Navy, the Canadian Navy, the Royal Netherlands Navy, the British Royal Navy, the US Coast Guard,

Proceedings of 25th ITTC – Volume II 625 and the US Navy. Naval Ship Code, NATO produced another In 2003 NATO initiated an effort to document, Guide to the Naval Ship Code develop a goal based standard for naval (NATO 2007b). The discussion of Chapter III vessels that could guide navies and in the Guide states “Due to the variety of classification societies in the development of available Naval Standards on stability and rules for naval vessels. The intent was to on-going work in other bodies to understand develop regulations for naval vessels that the dynamics of the stability problem and the paralleled the IMO regulations for commercial measure of safety provided by current vessels. (IMO regulations do not apply to standards, it was decided not to develop naval vessels.) In 2007, NATO issued several another detailed quasi-static stability documents relating to standards for classing standard.” Thus, the Naval Ship Code provides naval vessels, all under the umbrella of a only the most generic guidance with regard to Naval Ship Code (NATO, 2007a). The dynamic stability and capsize. introduction to the Naval Ship Code states, The Buoyancy and Stability chapter is “The overall aim of the Naval Ship Code is to divided into eight “Regulations.” numbered 0 provide a framework for a naval surface ship through 7. Regulations 1–7 are subdivided into safety management system based on and four sections: Functional Objectives, benchmarked against IMO conventions and Performance Requirements, Verification resolutions that embraces the majority of ships Methods, and Definitions (optional). Four of operated by Navies.” The code further goes on these Regulations (0 Goal, 1 General, 4 to state “. . . it therefore contains safety related Reserve of Stability, and 7 Provision of issues that correspond in scope to that which is Operational Information), explicitly mention covered by IMO publications but which reflect capsize or dynamic stability. The Regulation 0 the fundamental nature of naval ships.” Goal specifically states: Rudgley et al. (2005) provide an overview of the process and the overall philosophy for the 1 The buoyancy, freeboard, main sub- development of the Naval Ship Code. division compartment and stability charac- The Naval Ship Code is composed of ten teristics of the ship shall be designed, chapters: constructed and maintained to: .2 Provide adequate stability to avoid Chapter I General provisions capsizing in all foreseeable intact and Chapter II Structure damaged conditions, in the environ- Chapter III Buoyancy and Stability ment for which the ship is to operate, Chapter IV Machinery Installations under the precepts of good seamanship; Chapter V Electrical Installations Chapter VI Fire Safety The “Performance Requirements” listed under Chapter VII Escape, Evacuation and Regulation 1 General further elaborate: Rescue 4 The ship shall: Chapter VIII Radio communications .1 Be capable of operating in the Chapter IX Safety of Navigation environment defined in the Concept of Chapter X Carriage of Dangerous Operations Statement; Goods .2 Have a level of inherent seaworthiness Chapter III, Buoyancy and Stability, deals including motions tolerable by equip- with dynamic stability and capsize. This ment and persons onboard, control- chapter was developed in the second half of lability and the ability to remain afloat 2006 by a study group composed primarily of and not capsize;” representatives from: Australia, Canada, Italy, .3 Be designed to minimise the risk faced Netherlands, Spain and the United Kingdom, by hazards to naval shipping including with input from the Naval Stability Standards but not limited to the impact of the Working Group (NSSWG). In parallel to the

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environment causing dynamic capsize, correlation coefficients for many of these broach or damage to crew and equip- criteria parameters (e.g. GM, GZmax, GZ30°, ment, . . .” φrange, A0°-40°, A0°-φrange, etc.) were all higher .4 Be provided with operator guidance, as than 0.8 (the majority were higher than 0.9, required in Regulation 7 Operator many were close to 0.99). However, there was Guidance, to facilitate safe handling of no static stability parameter or criteria that had the ship. the highest correlation coefficient across all 12 The “Verification Methods” section of Regu- ships. This indicates that the current static- lation 1 General states: stability-based naval stability standards are not significantly deficient, at least for conventional 6 Verification that the ship complies with naval ship designs. However, it should be this chapter shall be by the Naval Ad- noted that there is no means of telling how ministration. much safety margin any of these ships have. 7 The burden of verification falls upon the The NSSWG is continuing its assessment Naval Administration. All decisions that of existing naval stability standards. It is affect compliance with the requirements anticipated that the FREDYN correlation will of this chapter shall be recorded at all be repeated with an updated version of the stages from concept to disposal and these code. However, this will require substantial records must be maintained throughout the computational effort and will not be under- life of the ship. taken lightly. Thus the Naval Ship Code contains no One navy that has been identified as specific dynamic stability or capsize criteria applying dynamic stability criteria is the US nor does it specify any procedures by which a Navy. Based on some model tests of vessel can be determined to be in compliance tumble-home hull forms in the late 1990s, it with the Code. Neither Regulation 4 Reserve was found that the criteria of DDS 079-1 (US of Stability nor Regulation 7 Provision of Navy 2003a) did not provide the equivalent Operational Information provides any margin against capsize for tumble-home ship additional detail on how the requirements are designs as it does for the traditional wall-sided to be met, this is left to each countries naval and flared designs. Therefore, an intensive authority. effort was instituted in 2000 to develop a The Naval Ship Code provides a dynamic-stability-based standard. This standardised ‘goal based’ framework, which standard is codified in two documents. The allows each naval authority to use its own first document is a succinct statement of the current static based or a performance based criteria (US Navy 2002) and the second standard to provide verification of a ship’s document provides the actual implementation ability to meet the overall stability goals of the standard. US Navy (2003b) is the defined in the code. current version of this second document, which is an annex to the primary standard. Developments Relating to Standards for The primary standard, the first version of the Navies. Among other topics, the NSSWG implementation document has in fact been has been examining existing naval stability incorporated in the American Bureau of standards with respect to a dynamic stability Shipping (ABS) Naval Vessel Rules (NVRs). assessment. Hughes (2006) presents prelimi- The US Navy dynamic stability criteria are nary results of this study. In the study a wide a relative criteria whereby the new vessel variety of static stability metrics (16 in total) design is assessed against an existing naval for 12 naval vessels have been correlated vessel designed for an equivalent mission. This against a dynamic stability assessment per- ensures that a frigate is not judged against an formed using an older version of the FREDYN aircraft carrier, or vice versa. The dynamic time domain simulation program. The stability criterion has five components, which

Proceedings of 25th ITTC – Volume II 627 are as follows: all of the sea states is not excessive, by limiting it to being no worse than the worst (a) The annual probability of capsize without risk for the benchmark ship. Component (c) is wind effects, for the appropriate range of intended to ensure that the ship has a region of sea states, when multiplied by a margin of the speed-polar plot where it can operate 1.10, is less than or equal to that of the without having to choose between having a equivalent mission benchmark ship. high risk of either capsize or broach, while (d) (b) For each sea state, the capsize probability ensures that there are no locations where the shall be determined for the specified range ship transitions too rapidly in speed or heading of modal periods. The worst-case capsize from safe operation to high risk of capsize, and probability for each sea state /modal finally, (e) ensures that there are no absolutely period multiplied by a factor of 1.10 shall unsafe areas on the capsize speed-polar plot be less than or equal to that of the worst where the ship has a 100 percent probability of capsize risk for the benchmark ship taken capsize. in the same sea state over the same range The implementation document has four of speeds, headings, and modal periods. components. The first defines the code to be (c) In any given sea state it is shown, on the used for the assessment and the physical capsize and broaching risk polar diagrams, model against which the code will be validated. that regions of high capsize probability, 60 The second component defines the process for percent or higher, are not adjacent to setting up the computational-model of a ship regions of high broaching probability, 60 for the dynamic stability simulations. The percent or higher. third component defines the code validation (d) Regions of zero capsize probability, as process against model tests and the criteria for shown on a capsize risk polar diagram, do the validation process. Finally, the last not transition to regions of 80 percent or component provides the details of the capsize higher capsize probability over a 5-knot risk assessment. range of speed or 15° heading change. The motivation for the US Navy (e) There shall be no region of 100 percent employing a relative capsize risk assessment capsize probability in the defined mission approach was the recognition that the sea states. simulation tools were not absolutely accurate, These criteria are applied over a range of sea but it was assumed that the biases of the states and modal periods. The sea states range employed computer code would be from 5 to 8, with sea states 7 and 8 being independent of the details of the hull form and subdivided into 3 significant wave heights, the environmental conditions. There are two each of which has 3 modal periods. For each major weakness of the US Navy relative significant wave height and modal period, an capsize criteria. The first is that there is no assessment of capsize probability is performed way of knowing what levels of safety or over a range of speeds, 0 to 30 kt in 5-kt margin against capsize the benchmark ship has. increments, and headings, 0° to 180°, in 15° The second relates to the assumption that the increments. For each speed-heading computational tools will have a uniform bias combination, 25 30-minute simulations are against all hull forms, actually it has been performed in a different realization of the sea found that this is not true. state being investigated, resulting in up to To supplement the relative capsize-risk 12-1/2 hours of simulated operation at each assessment methodology described, the US speed-heading combination. Navy is also investigating a methodology for Component (a) of the US Navy dynamic assessing annual and lifetime capsize risk stability criteria is intended to see that the based solely on regular wave-capsize model over-all capsize risk is acceptable. tests. This methodology relies on mapping the Component (b) ensures that the capsize risk in model test based capsize probabilities onto the

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628 joint probability distribution of a given wave by IMO: length and period in a given sea state and - An alternative procedure for the modal period. This joint probability assessment of compliance with Weather distribution is based on the work of Criterion with an experimental basis; Longuet-Higgins (1957). The results of these - The restructuring of the IS Code making calculations indicate that the lifetime capsize part of it mandatory; risk for a typical naval vessel are on the order - The refining and minor modifications to of a fraction of one percent. Intuitively, this IS Code; seems to be a reasonable absolute lifetime - And the revision of MSC Circ. 707 capsize risk. However, many issues relating to (MSC/Circ.707, 1995). the linear superposition of nonlinear experi- mental results via the decomposition of non- linear seas by means of a joint probability The Alternative Way of Assessment of distribution need to be resolved regarding this Weather Criterion Using an Experimental methodology. Basis. The original limits on the ship parameters used to set-up the Weather Crite- rion were identified as: 4.2 Review of Techniques for Merchant - Beam over draft ratio smaller than 3.5; Ships - Height of centre of gravity above waterline to draft ratio between -0.3 and The Revision of the Intact Stability Code. 0.5; The intact stability requirements for cargo and - Roll natural period smaller than 20 s. passenger ships, which are covered by the Intact Stability (IS) Code (IMO, 2002) have The development of an alternative assess- undergone a large revision process in the last ment for ships with parameter values outside five years. this range was later extended to all ships with The IS Code contains design criteria and the authorisation of the Administration and other recommendations to be verified in a was given high priority. range of loading conditions. The revision Using studies reported in SLF47/6/18 process at International Maritime Organization (2004) and SLF49/5/5 (2007), an interim (IMO), started in 2001 (SLF44/INF.6, 2001), guideline for the alternative assessment of concerned the need to update and tune some compliance with Weather Criterion with an coefficients of the Weather Criterion in view experimental basis was produced and is con- of its excessive effect in determining the tained in MSC.1/Circ.1200 (2006), whereas limiting vertical centre of gravity for ships the explanatory notes are given in MSC.1/ with large values of the beam-over-draft-ratio. Circ.1227, (2007). This allows the evaluation To resolve these issues, a series of of the roll-back angle φ1 by means of experiments (Fujino, et al., 1993, Francescutto, experiments conducted on a scale model of the et al., 2001) were conducted for the evaluation ship, evaluated in regular beam waves having the steepness table corrected in the low of the roll-back angle φ1, under the action of beam waves (for details see Francescutto, frequency range as in Fig. 4.1. In the case of 2004). vessels with large roll periods, for example This change was considered a good greater than 20 s, it is not possible to test opportunity to update the IS Code’s founda- models at the required size and nominal wave tions, putting them on a more physical basis, steepness in most model basins. This required through the development of new performance the development of a procedure for the based criteria (PBC) originally intended to evaluation of the maximum roll amplitude in replace the older prescriptive criteria. large amplitude waves starting from the The following tasks have been completed experimental results in low amplitude waves.

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This extrapolation is a delicate part of the rolling. The results of the worked example procedure; two different methodologies were reported in the Explanatory Notes MSC.1/Circ. developed and can be accepted; the first 1227, (2007) seem to indicate that the limiting substantially reproducing the procedure used metacentric height has a non-negligible in the original development of Weather spreading. This is principally connected with Criterion, while the second is based on the the different results in terms of the wind lever, parameter identification technique. At the due to the fact that the drift test analysis gives same time it is also possible to evaluate the a very high position of the centre of wind parameters (constant wind and gust hydrodynamic reaction (around waterline and levers) through combined experiments. eventually above waterline). These results are awaiting confirmation (Ishida, et al,, 2006, Umeda et al 2006c).

Restructuring IS Code Making Some Parts Mandatory. Although presently an IMO recommendation, several parts of the IS Code are mandatory in many instances. However, their particular status allowed some alternatives presently included in the rules adopted by several Administrations. At MSC78, on the basis of a formal safety assessment study (MSC78/24/1, 2003), it was decided to restructure the code into three parts: - Part A, containing “design criteria appli- cable to all types of ships” to become mandatory; - Part B, containing recommendations for Figure 4.1 Wave steepness as a Function of certain types of ships; Roll Natural Period as in Standard Weather - Part C containing symbols and terminol- Criterion and as Adopted in the Alternative ogy and explanatory notes. Assessment with an Experimental Basis This task was accomplished at SLF50 in 2007 with the proposal to make part A mandatory both under SOLAS and ICLL to accelerate its For the combined tests, the above-water entering into force. topsides are tested in a wind tunnel to measure the resultant wind force and the height of its point of application. Once this is known, the IS Code Present Situation. There were under-water hull is tested in a towing tank other pending issues connected with the fact (drift tests) investigating the drift speed that the mandatory IS Code made the adoption required to give a hydrodynamic reaction of some alternatives currently used by equal to wind force and identifying the depth Administrations not possible. The most of its point of application. Simplified tests are important is connected with the required possible to determine the dependence on the minimum value for the angle of maximum transverse inclination and the assumption of righting lever. During the discussion made at half draft (present value) for the point of SLF50, the application of the Offshore Supply application selected for the hydrodynamic Vessels rule, allowing the reduced angle of reaction. maximum righting lever down to 15 deg, with The interim guidelines allow any an increase of dynamic stability (area under combination of partial procedures for wind/ GZ curve) up to the maximum, was considered

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630 a viable alternative. In the course of the and relevant comments by Italy (SLF50/4/12, discussion, the problem of the equivalent level 2007), an updated plan of action was made. of safety was raised. This does not merely constitute a return to the original scope of the revision of the Intact The Equivalent Level of Safety. The Stability Code, since in the meantime the safety level guaranteed to ships complying levels of knowledge and consciousness of the with the stability criteria is generally unknown. possibilities and limits of simulation In addition, it is clear that it is unequally procedures have greatly improved. This is also distributed among different ship typologies due to the second “cooperative benchmark and even inside a given ship typology, it experiment” launched by 24th ITTC calling appears to be strongly dependent on ship size. for comparison of predicted basic quantities A study conducted by Umeda and Yoshinari, with high quality experimental results. This (2003) on the capsizing probability in beam action was motivated by the substantial failure waves of a sample of ships marginally in the capability of simulation codes to complying with the provisions of Intact quantitatively simulate the global extreme Stability Code revealed that the capsizing behaviour of ships in rough weather shown probability is spread in a wide interval during previous benchmarks. Following this covering many orders of magnitude. Only the outcome, ITTC could proceed in the development of performance-based criteria can development/ revision of the procedures for allow a resolution of this problem. testing and simulation, which are expected to play a major role in future development of Operational Guidelines to Avoid PBCs. Dangerous Phenomena in Waves. Together The following distinctions were made at with the intact stability criteria, IMO has SLF50 (SLF50/4/4, 2007; SLF50/4/12, 2007) developed operational guidance for avoiding regarding the stability problems: dangerous phenomena in following and quartering waves (MSC/Circ. 707, 1995). In relation to the consequences: A new MSC Circular (MSC.1/Circ.1228, - Partial stability failure 2007) ship-independent and of qualitative - Total stability failure nature was developed with the following In relation to the modes: changes: - Restoring arm variations problems, like - Simplification, to avoid excessive and parametric rolling and pure loss of partly unjustified warnings to the master; stability - The inclusion of the consideration of - Stability under dead ship conditions parametric rolling in head waves. - Manoeuvring-related problems in waves like broaching The formulation of ship-specific guidance was In relation to the implementation: left for future developments. - Probabilistic versus deterministic PBC - Probabilistic versus deterministic paramet- Future Developments: Performance-Based ric criteria Criteria (PBC). At SLF50 the International In relation to the needs: Intact Stability Code was concluded by the - Guidelines for the development, use, and Sub-Committee and successively approved by benchmarking of direct simulation tools; MSC as the 2008 IS Code. The need for the - Guidelines for alternative model testing, development of new criteria, based on more in a way similar to that already followed realistic physical approaches was stressed. in the case of Weather Criterion (MSC.1/ Following important submissions by several Circ.1200 and MSC.1/Circ.1227); delegations and in particular by Japan, the - Simplified physically sound semi-analyti- Netherlands and the USA (SLF50/4/4, 2007) cal models addressing, separately, particu-

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lar phenomena. or insufficiently, covered by the existing The Updated Plan of Action. At SLF50 criteria, as assessed by way of a “vulnerability a rational updated plan of action was decided: criteria.”

- Develop vulnerability criteria to identify Progress in the Development of the possible susceptibility of a ship to partial (excessive roll angles/accelera- Numerical Methods. Reviewing the results tions) or total (capsizing) stability failures of the comparative studies conducted during for each mode. previous two terms by the ITTC Specialist - Develop procedures for direct assessment Committee on Ship Stability in Waves, it of: appears that the progress in the development of simulation codes obtaining the physical 1 Stability failures under dead ship model characteristics from other sources conditions; (captive experiments), progressed faster than 2 Stability failures in following seas that of the fully hydrodynamic simulation associated with matters related to codes, where all or most of the physical model stability variation in waves, in characteristics are calculated by the code itself. particular reduced righting levers of a As far as the beam sea case is concerned, ship situated on a wave crest; the introduction of a capsize index and the 3 Stability failures caused by parametric evaluation of the probability of capsizing resonance, including consideration of under the action of stochastic beam wind and matters related to large accelerations waves is presented (Bulian and Francescutto, and loads on cargo and stability 2006a; SLF49/5/5, 2006; Paroka and Umeda, variation in waves; and 2006). The approach constitutes a stochastic 4 Stability failures caused by broaching generalization of present Weather Criterion including consideration of matters with improved physical basis. related to manoeuvrability and course keeping ability as they affect stability; Concerning the longitudinal/quartering waves case, an attempt to validate numerical - Develop: simulation of parametric rolling is presented in 1 Standard requirements for on-board SLF/49/5/7 (2006). However, further valida- guidance; tion of numerical modelling are required to 2 Criteria for certain types of ships; and realize direct assessment as an alternative 3 Implementation plan for incorporating means to the prescriptive criteria in the Intact a new generation intact stability criteria Stability Code. into the IS Code as well as parametric In SLF49/5/2 (2006) and SLF49/INF.3 (simplified) criteria. (2006) a probabilistic intact stability criterion The idea of vulnerability criteria is of for parametric rolling and pure loss of stability paramount importance in the frame of phenomena is presented. It is based on the developing criteria to improve ship safety, or definition of a Capsizing Index by a procedure making safety improvement more “cost- based on the fact that the significant wave effective” against modes of failure not covered height should allow that the residual area by present criteria. It could avoid the need for under the still water righting lever curve from indiscriminate generalized application of the maximum angle to the point of vanishing heavy computational or experimental proce- stability during one simulation exceeds three dures. times the standard deviation of that area Once developed, the new generation of obtained from several simulations. In stability criteria could indeed be applied to SLF50/INF.2 (2007) an improved approach is certain ships that due to their typology and/or presented. size, could be more susceptible to hazards not, Considering parametric rolling in general, it seems that the predictions of a threshold and

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632 amplitude above threshold may be of failure levels has been proposed. The acceptable accuracy when regular waves are methodology caters for the probabilistic part of considered (Bulian and Francescutto, 2006b; a risk-based assessment. Hashimoto et al., 2008). However, further The application of first- and partly research is needed as far as the irregular wave second-order reliability methods (FORM and case is concerned. SORM) to estimate extreme ship motions and Analytical formulae for the prediction of capsizing was considered by Jensen (2007), asymmetric surging and surf-riding in pure Kogiso and Murotsu (2008) and Spanos, et al. regular following seas, which often forerun (2008). broaching, were presented in Spyrou (2006). A methodology for the direct assessment of surf-riding in regular stern quartering waves 5 CONCLUSIONS AND RECOMMEN- was presented in Umeda, et al. (2006a). The DATIONS document suggests that numerical predictions without captive model test data for each subject ship are potentially conservative. 5.1 General Technical Conclusions

Progress in the Development of Intact Stability. A state-of-the-art review Experimental Methods. The development of has been carried out concerning experimental experimental assessment procedures relies on techniques to model extreme motions, broach- having reliable procedures for the simulation ing and capsizing of intact ships in waves, of large amplitude motions and capsizing; or at including parametric rolling. least for the evaluation of relevant quantities The Procedure 7.5-02-07-04.1 “Model connected to “conventional” assessment rules. Tests on Intact Stability” has been updated and These procedures should be standardized extended to cover head-sea parametric rolling. following the guidelines indicated by ITTC. Experimental data for future benchmark test- A notable example of progress in this ing study of time domain codes were direction is the development of the identified. experimental procedure for the alternative assessment of Weather Criterion. However, Damage Stability. State-of-the-art roll damping is still a current problem, both in reviews have been carried out concerning prediction and in model/full-scale transfer. numerical and experimental techniques to predict extreme motions and capsizing of Progress in the Development of damaged ships in waves with particular focus Probabilistic Methods. For quantifying the on the prediction of time-to-flood calculations. probability of broaching in irregular waves Responding to the request from the IMO, Umeda et al (2007) proposed a methodology prediction capabilities of numerical codes for by integrating a joint probability density of time-to-flood have been investigated. First a local wave height and wave period within the comparative study on a flooded barge was deterministic danger threshold and validated it executed and distinct differences between successfully with Monte Carlo simulations in prediction models and experimental results the time domain. with respect to flooding rates are found. Second, complex geometry data of a large During the EU project SAFEDOR a novel passenger ship were provided and the relevant methodology for probabilistic assessment of numerical runs were executed for evaluating various types of ship instability (in the time-to-flood predictions. “short-“ as well as in the “long-term”) has been developed, exploiting the groupiness Supported by the EU project SAFEDOR, a characteristic of high waves (Themelis and benchmark study on the prediction of extreme Spyrou, 2007). The setting of warning and motions and capsizing of damaged RoPax

Proceedings of 25th ITTC – Volume II 633 ships in waves has been conducted. The Thomas III, W. L., 1999, “Dynamic numerical estimations of the survival wave Capsize Vulnerability: Reducing the height were found to be sensitive with respect Hidden Operational Risk“, Trans. SNAME, to the ship loading condition and the periods of 107:245–80. the incident waves, while less sensitive with Armaoğlu, E., Ayaz, Z., Vassalos, D. and, respect to the assumptions for the discharge Katayama, T., 2006, “On Manoeuvrability coefficients. No conclusions could be derived of Semi-Displacement Craft in Astern for the effect of the viscous roll damping. Two Seas” Proc. STAB 2006, Rio de Janeiro, of the benchmarked methods did show pp.383–393. satisfactory prediction capability, but overall performance calls for further improvements of Ayaz, Z., Vassalos, D. and Spyrou, K. J., 2006, employed methods and codes. “Manoeuvring Behaviour of Ship in Extreme Astern Seas“, Ocean Engineering, Stability Safety Assessment. A 33:2381–2434. state-of-the- art review has been carried out Belenky, V., Weems, K. M. and Paulling, J. R., concerning intact stability safety assessment 2003, “Probabilistic Analysis of Roll methods. Regarding naval ships, one navy has Parametric Resonance in Head Seas“, Proc. already implemented performance-based intact STAB 2003, Madrid, pp.325–340. stability criteria. For merchant ships, the IMO implemented a procedure for the alternative Belenky, V., Yu, H.-C. and Weems, K.M., 2006, assessment of the weather criterion on an “Numerical Procedures and Practical experimental basis and prepared a plan of Experience of Assessment of Parametric action for the development of Roll of Container Carriers“, Proc. STAB performance-based criteria. 2006, Rio de Janeiro, pp. 119–130. Bulian, G. and Francescutto, A., 2006a, ”Safety and Operability of Fishing 5.2 Recommendation to the Conference Vessels in Beam and Longitudinal Waves“, International J. Small Craft Technology, Adopt the revised Procedure 7.5-02-07-04.1 148: 1-15. “Model Tests on Intact Stability”. Bulian, G. and Francescutto, A., 2006b, “On the Effect of Stochastic Variations of Restoring Moment in Long-Crested 6. REFERENCES AND NOMENCLA- Irregular Longitudinal Sea,” Proc. STAB TURE 2006, Rio de Janeiro, pp. 131–146.

Bulian, G., Francescutto, A. and Lugni, C., 6.1 References 2004, “On the Nonlinear Modelling of Parametric Rolling in Regular and Alford, L. K., Troesch, A. W. and McCue, L. Irregular Waves” International Ship- S., 2005, “Design Wave Elevations Lead- building Progress, 51:173–203 ing to Extreme Roll Motion”, Proc. 8th Bulian, G., Francescutto, A. and Lugni, C., ISSW, Istanbul, CD. 2006, “Theoretical, Numerical and Alford, L, K., Troesch, A. W. and Khalid, M. Experimental Study on the Problem of S., 2006, “Results Using Response- Ergodicity and ‘Practical Ergodicity’ with Tailored Design Waves in Simulations of an Application to Parametric Roll in Extreme Roll of Multi-Hull Ships,” Proc. Longitudinal Long Crested Irregular STAB 2006, Rio de Janeiro, pp. 269–277. Sea“ Ocean Engineering, 33:1007–1043. Alman, P., Minnick, P. V. Sheinberg, R. and Bulian, G., Francescutto, A., Umeda, N. and

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Hashimoto, H., 2008, ”Experimental Proc. U.S. Coast Guard Vessel Stability Investigation on Stochastic Parametric Symposium, New London. Rolling for a Post-Panamax Container- Fujiwara, T. and Ikeda, Y., 2007, “Effects of ship,” Proc. OC 2008 , Osaka, pp. 371-382. Roll Damping and Heave Motion on Burcher, R. K. 1990, “Experiments into the Heavy Parametric Rolling of a Large Capsize of Ships in Head Seas”. Proc. Passenger Ship in Beam Waves” Proc. 9th STAB 90, Naples, 1: 82–89. ISSW, Hamburg, CD Cho S. K., Hong, S.Y. and Kyoung, J. H. , HARDER, 2000–2003, “Harmonization of 2006, “The Numerical Study on the Rules and Design Rational,” European Coupled Dynamics of Ship Motion and Commission Research Project, DG Flooding Water“, Proc. STAB 2006, Rio de XII-BRITE. Janeiro, pp. 599-605. Hashimoto, H., Umeda, N., Matsuda, A. and Dallinga, R. P., Blok, J. J. and Luth, H. R., Nakamura, S., 2006, “Experimental and 1998, ”Excessive Rolling of Cruise Ships Numerical Studies on Parametric Roll of a in Head and Following Waves,” Proc. Post-Panamax Container Ship in Irregular RINA International Conference on Ship Waves“, Proc. STAB 2006, Rio de Janeiro, Motions & Manoeuvrability, London. pp.181–190. Estonia Debate, 2007, Estonia International Hashimoto, H., Umeda, N. and Sakamoto, G., Workshop. The Ship Stability Research 2007, “Head-Sea Parametric Rolling of a Centre, Department of Naval Architecture Car Carrier,” Proc 9th ISSW, Hamburg, and Marine Engineering, University of CD. Glasgow, UK. Hashimoto, H., Umeda, N. Ogawa, Y., Taguchi, France, W. N., Levadou, M., Treakle, T. W., H., Iseki, T., Bulian, G., Toki, N., Ishida, S. Paulling, J. R., Michel, R. K. and Moore, C., and Matsuda, A., 2008, “Prediction 2003, “An Investigation of Head-Sea Methods For Parametric Rolling with Parametric Rolling and its Influence on Forward Velocity and Their Validation— Container Lashing Systems“, Marine Final Report of SCAPE Committee (Part Technology, 40(1):1–19. 2),” Proc. OC2008, Osaka, pp. 265-275. Francescutto, A., 2001, “An Experimental Hughes, T. 2006, “Naval Stability Standards Investigation of Parametric Rolling in Working Group: Intact Stability Standards Head Waves“, J. Offshore Mechanics and Assessment. Phase 1,” NSSWG Report, Arctic Engineering, 123:65–69. 74p. Francescutto, A., 2004, “Intact Ship Ikeda, Y., Munif, A., Katayama, T. and, Stability—The Way Ahead“, Marine Fujiwara, T. 2005, “Large Parametric Technology, 41:31–37. Rolling of a Large Passenger Ship in Beam Seas and Role of Bilge Keel in Its Francescutto, A., Serra, A. and Scarpa, S., Restraint,” Proc. 8th ISSW, Istanbul, CD. 2001, “A Critical Analysis of Weather Criterion for Intact Stability of Large IMO, 2002, “Code on Intact Stability for All Passenger Vessels“, Proc. OMAE 2001, Types of Ships Covered by IMO Rio de Janeiro. Instruments,” IMO Res. A.749(18), as amended by MSC.75(69), London, IMO. Fujino, M., Fujii, I.,Hamamoto, M., Ikeda, Y., Ishida, S. Morita, T., Tanai, K. and Umeda, Ishida, S., Taguchi, H. and Sawada, H., 2006, N., 1993, “Examination of Roll Damping “Evaluation of the Weather Criterion by Coefficients and Effective Wave Slope Experiments and its Effect to the Design of Coefficients for Small Passenger Crafts“, a RoPax Ferry,” Proc. STAB 2006, Rio de

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Janeiro, pp. 9–16. Monohull in Following and Stern Quarter- ing Seas“, Proc. 8th ISSW, Istanbul, CD.. ISSW, 2005, Proceedings of the 8th International Ship Stability Workshop, Marón, A., Carrillo, E., Valle, J., Prieto, M. E., Istanbul Technical University, Faculty of Gutiérrez, C. and Taboada, M. 2006, Naval Architecture and Ocean Engineering, “Investigation on the Capsizing of a Small SDKM Maslak Campus, Istanbul, Turkey, Fishing Vessel in Following Seas“, Proc. October 6–7, 2005 STAB 2006, Rio de Janeiro, pp.633–640. ISSW, 2007, Proceedings 9th International Matsuda, A., Hashimoto, H. and Umeda, N., Ship Stability Workshop, Germanischer 2006, “Experimental and Theoretical Study Lloyd, Hamburg, Germany, August 30–31, on Critical Condition of Bow-Diving,” 2007 Proc. STAB 2006, Rio de Janeiro, pp.455-461. Jankowski, J. and Laskowski, A. 2006, “Capsizing of Small Vessel Due to Waves Matsuda, A., Hashimoto, H. and Momoki, T. and Water Trapped on Deck“, Proc. STAB 2007, “Non-linear Hydrodynamic Force 2006, Rio de Janeiro, pp. 867-875. Measurement System in Heavy Seas for Broaching Prediction,” Proc. 9th ISSW, Jensen, J. J., 2007, “Efficient Estimation of Hamburg, CD. Extreme Nonlinear Roll Motions using the First Order Reliability Method (FORM),” J. Matusiak, J., 2003, “On the Effects of Wave Marine Science and Technology, 12: Amplitude, Damping and Initial Condi- 191-202. tions on the Parametric Roll Resonance“, Proc. STAB 2003, Madrid, pp.341–348. Katayama, T. and Ikeda, Y., 2005, “An Experimental Study of Fundamental Char- McTaggart, K. A., 2000, “Ship Capsize Risk in acteristics of Inflow Velocity from Damag- a Seaway Using Fitted Distributions to ed Opening,” Proc. 8th ISSW, Istanbul, Roll Maxima“, J. Offshore Mechanics and CD. Arctic Engineering, 122:141–146. Kosigo, N. and Murotsu, Y. 2008, McTaggart, K. A. and de Kat, J. O., 2000, “Application of First Order Reliability “Capsize Risk of Intact Frigates in Method to Ship Stability—Final Report of Irregular Seas“, Trans. SNAME, SCAPE Committee (part 5),” Proc. OC 108:147–77. 2008, Osaka, pp 299-306. MSC/Circ.707, 1995, “Guidance to the Master Lee, Y.-W., McCue, L., Obar, M. and Troesch, for Avoiding Dangerous Situations in A., 2006, “Experimental and Numerical Following and Quartering Seas,” IMO, Investigation into the Effects of Initial London. Conditions on a Three Degree of Freedom MSC.1/Circ.1200, 2006, “Interim Guidelines Capsize Model,” J. Ship Research, for Alternative Assessment of Weather 5(1):63–84. Criterion,” IMO, London. Levadou, M. and Veer, R. van’t, 2006, MSC.1/Circ.1227, 2007, “Explanatory Notes “Parametric Roll and Ship Design,” Proc. to the Interim Guidelines for Alternative STAB 2006, Rio de Janeiro, pp. 191–206. Assessment of the Weather Criterion,” Longuet-Higgins, M. S., 1957, “The Statistical IMO, London. Analysis of a Random, Moving Surface,” MSC.1/Circ.1228, 2007, “Revised Guidance to Phil. Trans. Roy. Soc., A 249:321–87. the Master for Avoiding Dangerous Lundbäck, O., 2005, “An Investigation of Situations in Adverse Weather and Sea Hydrodynamic Forcing on A Semi-Planing Conditions,” IMO, London.

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MSC78/24/1, 2003, “Revision of the Code on Waves,” Proc. 19th Symp. Naval Hydro., Intact Stability“, Submitted by Germany, Seoul, pp.93–111. IMO, London. Oh, I.G., Nayfeh, A.H. and Mook, D.T., 2000, Munif, A., Ikeda, Y., Fujiwara, T. and “A Theoretical and Experimental Katayama, T. 2006, “Parametric Roll Investigation of Indirectly Excited Roll Resonance of a Large Passenger Ship in Motion in Ships in Longitudinal Waves,” Dead Ship Condition in All Heading Phil. Trans. Royal Soc. London, A, Angle“, Proc. STAB 2006, Rio de Janeiro, 358:1853–1881. pp.81–88. Olivieri, A., Campana, E. F., Francescutto, A. Nabavi, Y., S. M. Calisal, A. Akinturk and V. and Stern, F., 2006, “Beam Seas Tests of Klaptocz (2006) A Computational Two Different Ship Models in Large Investigation of the Three Dimensional Amplitude Regular Waves,” Proc. STAB Geometric Parameters’ Effects on the 2006, Rio de Janeiro, pp. 419–433. Discharge Rate of a Ship Opening. Proc. Papanikolaou, A. and Spanos, D., 2008, STAB 2006, Rio de Janeiro, pp. 617-624. “Benchmark Study on Numerical Codes NATO, 2007a, “Buoyancy, Stability and for the Prediction of Damage Ship Stability Controllability. Chapter III of Naval Ship in Waves,” Proc. 10th ISSW, Daejon, CD. Code“, NATO Naval Armaments Group, Paroka, D. and Umeda, N., 2006, “Capsizing Maritime Capability Group 6, Specialist Probability Prediction for a Large Team on Naval Ship Safety and Passenger Ship in Irregular Beam Wind Classification, Allied Naval Engineering and Waves: Comparison of Analytical and Publication ANEP – 77, vii+121 p. Numerical Methods,” J. Ship Research, NATO, 2007b, “Guidance on NSC Chapter III 50:371–377. Buoyancy and Stability,” Part B: Perez-Rojas, L., Pavón, C. L., Arribas, F. P. Application, Chapter 3, Guide to the and Landaluce, A. M., 2007, “On the Naval Ship Code, NATO Naval Experimental Investigation on the Armaments Group, Maritime Capability Capsizing of Small Fishing Vessels,” Proc. Group 6, Specialist Team on Naval Ship 9th ISSW, Hamburg, CD. Safety and Classification, 91 p. Rahola, J., 1939, “The Judging of the Stability Neves, M.A.S., Perez, N. and Lorca, O. 2002, of Ships and the Determination of the “Experimental Analysis on Parametric Minimum Amount of Stability Especially Resonance for Two Fishing Vessels in Considering the Vessel Navigating Finnish Head Waves,” Proc. 6th ISSW, New York. Waters,” PhD Thesis, Technical University Neves, M.A.S. and Rodriguez, C.A. 2005, of Finland, Helsinki, viii+232 p. “Stability Analysis of Ships Undergoing Rudgley, G., ter Bekke, E. C. A., Boxall, and Strong Roll Amplifications in Head Seas,” Humphrey, R., 2005, “Development P. of a Proc. ISSW, Istanbul, CD. NATO Naval Ship Code,” Proc. RINA Ogawa, Y., Kat, J. O. de and Ishida, S., 2006, Conference on Safety Regulations and “Analytical Study of the Effect of Drift Naval Class II, RINA, London, United Motion on the Capsizing Probability under Kingdom, 8 p. Dead Ship Condition,” Proc. STAB 2006, Ruponen, P., 2006a, “Pressure Correction Rio de Janeiro, pp.29-36. Method for Simulation of Progressive Oh, I. G., Nayfeh, A. H. and, Mook, D. T. 1992, Flooding and Internal Air Flows,” Ship “Theoretical and Experimental Study of Technology Research, 53:63–73. the Nonlinearly Coupled Heave, Pitch, and Ruponen, P., 2006b, “Model Tests for the Roll Motions of a Ship in Longitudinal

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Progressive Flooding of a Box-shaped SLF44/INF.6, 2001, “Weather Criterion for Barge,” HUT Ship Laboratory Report, Large Passenger Vessels,” Submitted by Helsinki, Finland. Italy, IMO, London. Ruponen P., 2007, “Extensions to a Pressure SLF47/6/18, 2004, “Guidelines for Model Correction Method for Simulation of Testing of Intact Stability—Experimental Progressive Flooding,” Proc. 9th ISSW, Approach to Evaluate the Relevant Factors Hamburg, CD. for the Calculation of the Roll Angle θ1” Submitted by Italy and Japan, IMO, Ruponen, P. and Routi, A.L. 2007, “Time London. Domain Simulations of Cross-Flooding for Air Pipe Dimensioning,” Proc. 9th ISSW, SLF49/5/2, 2006, “Proposal of a Probabilistic Hamburg, CD. Intact Stability Criterion,” Submitted by Germany, IMO, London. SAFEDOR, 2005–2008, “Design, Operation and Regulation for Safety“, European SLF49/5/5, 2006, “Proposal of Methodology Union research project of the FP6 of Direct Assessment for Stability Under Sustainable Surface Transport Programme, Dead Ship Condition,” Submitted by Japan, http://www.safedor.org, 2005–2008. IMO, London. Santos T. A. and Guedes Soares, C., 2006, SLF49/5/7, 2006, “Remarks of Numerical “Study of the Dynamics of a Damaged Modelling for Parametric Rolling,” Passenger Ro-Ro Ship,” Proc. STAB 2006, Submitted by Japan, IMO, London. Rio de Janeiro, pp. 587-597. SLF49/5/7/Corr.1, 2006, “Remarks of Sarchin, T. H. and Goldberg, L. L., 1962, Numerical Modelling for Parametric “Stability and Buoyancy Criteria for U. S. Rolling,” Submitted by Japan, IMO, Naval Surface Ships“, Trans. SNAME, London. 72:418–58. SLF49/INF.3, 2006, “Benchmarking for a Schreuder, M., 2005, “Time Simulation of the Proposal of a Probabilistic Intact Stability Behaviour of Damaged Ships in Waves,” Criterion,” Submitted by Germany, IMO, Thesis for Licentiate of Engineering, London. Department of Shipping and Marine SLF50/4/4, 2007, “Framework for the Technology, Chalmers University of Development of New Generation Criteria Technology, Göteborg, Sweden. for Intact Stability,” Submitted by Japan, Silva, S. R. and Guedes Soares, C., 2000, The Netherlands and the USA, IMO, “Time Domain Simulation of Parametri- London. cally Excited Roll in Head Seas,” Proc. SLF50/4/12, 2007, “Comments on the STAB 2000, Launceston, B:652–664. Development of New Generation Intact Skaar D., Vassalos, D. and Jasinowski, A., Stability Criteria,” Submitted by Italy, 2006, “The Use of Mesh Less CFD IMO, London. Methods in Modelling Progressive SLF50/INF.2, 2007, “Proposal on Additional Flooding and Damage Stability of Ships,” Intact Stability Regulations,” Submitted by Proc. STAB 2006, Rio de Janeiro, pp. Germany, IMO, London. 625-632. Spanos, D. and Papanikolaou, A., 2005, Skomedal, S. G., 1982, “Parametric Excitation “Numerical Simulation of a Fishing Vessel of Roll Motion and Its Influence on in Parametric Roll in Head Sea,” Proc. 8th Stability,” Proc. STAB ‘82, Tokyo, pp. ISSW, Istanbul, CD. 113–125. Spanos, D. and Papanikolaou. A., 2007, “On

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the Time to Capsize of Damaged Broaching in the light of Local and Global RoRo/Passenger Ship in Waves,” Proc. 9th Bifurcation Analysis,” Proc. STAB 2006, ISSW, Hamburg, CD. Rio de Janeiro, pp. 353–362. Spanos, D., Papanikolaou, A. and Papatzanakis, Umeda, N., Hori, M., Aoki, K., Katayama, T. G., 2008, “Risk-based Onboard Guidance and Ikeda, Y. 2006b, “Experimental to the Master for Avoiding Dangerous Investigation on Capsizing and Sinking of Seaways,” Proc. OC 2008, Osaka, pp a Cruising Yacht in Wind,” Proc. STAB 249-256. 2006, Rio de Janeiro, pp. 659–667. Spyrou, K.J., 2006, “Asymmetric Surging of Umeda, N., Ueda, J., Paroka, D., Bulian, G. Ships in Following Seas and Its and Hashimoto, H., 2006c, “Examination Repercussions for Safety,” Nonlinear of Experiment-Supported Weather Dynamics, 43:149–172. Criterion with a RoPax Ferry Model,” Conference Proc. Japan Society of Naval STAB, 2006, “Proceedings 9th International Architects and Ocean Engineers, 2:5-8. Conference on Stability of Ships and Ocean Vehicles,” Rio de Janeiro, Brazil, Umeda, N., Shuto, M. and Maki, A., 2007, September 25–29, 2006. “Theoretical Prediction of Broaching Probability for a Ship in Irregular Astern Taguchi, H., Ishida, S., Sawada, H. and Seas,” Proc. 9th ISSW, Hamburg, CD. Minami, M., 2006, “Model Experiment on Parametric Rolling of a Post-Panamax US Navy, 2002, “Stability Criteria for New Containership in Head Waves,” Proc. Monohull Surface Combatants,” STAB 2006, Rio de Janeiro, pp. 147–156. Department of the Navy, Naval Sea Systems Command, 7 p. Themelis, N. and Spyrou, K.J., 2007, “Probabilistic Assessment of Ship US Navy, 2003a, “Design Data Sheet DDS Stability,” Trans. SNAME. 079-1, Stability and Buoyancy of U.S. Naval Surface Ships,” Version 1.21, 81 p. Umeda, N., 2007, “Application of CFD to Ship Capsizing Prevention”, Contract US Navy, 2003b, “Dynamic Stability number: N00014-06-1-0646, ONR Report Assessment Tools and Methodologies for of FY2007. New Monohull Displacement Surface Combatant Ships, Stage 1,” Rev 2, 13 p. Umeda, N. and Yoshinari, K., 2003, “Examination of IMO Weather Criterion in Valanto, P., 2007, “New Research into the MV the Light of Capsizing Probability ESTONIA Disaster,” Proc. 9th ISSW, Calculation,” Conference Proc. Society of Hamburg, CD. Naval Architects of Japan, 1:65–66. Vassalos, D. and Jasionowski, A., 2007, Umeda, N., Hashimoto, H., Vassalos, D., “SOLAS 2009—Raising the Alarm,” Proc. Urano, S. and Okou, K. 2003, “Nonlinear 9th ISSW, Hamburg, CD Dynamics on a Parametric Roll Resonance Walree, F. van, 2007, “Benchmark Study of with Realistic Numerical Modelling,” Proc. Numerical Codes for the Prediction of STAB 2003, Madrid, pp. 281-290. Time to Flood of Ships: Phase 1,” ITTC Umeda, N., Hashimoto, H., Paroka, D. and Stability in Waves Committee. Hori, M. 2005, “Recent Developments of Walree F. van, and Carette, N. 2008a, Theoretical Prediction on Capsizes of “Benchmark Study of Numerical Codes for Intact Ships in Waves,” Proc. 8th ISSW, the Prediction of Time to Flood of Ships: Istanbul, CD. Phase 2“, ITTC Stability in Waves Umeda, N., Hori, M. and Hashimoto, H., Committee. (to be issued). 2006a, “Theoretical Prediction of

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Walree F. van and Carette, N. 2008b, ICLL International Convention on Load “Benchmark Study of Numerical Codes for Lines the Prediction of Time to Flood of Ships: IMO International Maritime Phase 2,” Proc. 10th ISSW, Daejeon, 8p. Organization ISSW International Ship Stability Walree, F. van and Kat, J. O. de, 2006, Workshop “Forensic Research into the Loss of Ships MSC Maritime Safety Committee by Means of a Time Domain Simulation OC Osaka Colloquium Tool,” Proc. STAB 2006, Rio de Janeiro, OMAE International Conference on pp. 641-657. Offshore Mechanics and Arctic Walree, F. van and Papanikolaou, A. 2007, Engineering “Benchmark Study of Numerical Codes for PBC Performance Based Criteria Prediction of Time to Flood of Ships: RINA Royal Institution of Naval Phase I,” Proc. 9th ISSW, Hamburg, CD. Architects SiW Specialist Committee on Stability Yang, S., Fan, S., Nie, J., Lu, Z. and Yu, Z., in Waves 2008, “Experimental and Numerical SLF Sub-Committee on Stability and Investigation on Parametric Rolling in Load Lines and on Fishing Vessels Regular Head Waves for a Large Safety Containership,” Proc. OC2008, Osaka, pp. SNAME Society of Naval Architects and 359-363. Marine Engineers SOLAS International Convention for the Safety of Life at Sea

SPH Smoothed Particle Hydrodynamics 6.2 Nomenclature STAB International Conference on Stability of Ships and Ocean CFD Computational Fluid Dynamics Vehicles DOF Degrees of Freedom VOF Volume of Fluid

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