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About this book

This book contains a selection of research papers presented at the 11th and 12th International Ship Stability Workshops (Wageningen, 2010 and Washington DC, 2011) and the 11th International Conference on Stability of Ships and Ocean Vehicles (Athens, 2012). The book is directed toward the ship stability community and presents innovative ideas concerning the understanding of the physical nature of stability failures and methodologies for assessing ship stability. Particular interest of the readership is expected in relation with appearance of new and unconventional types of ships; assessment of stability of these ships cannot rely on the existing experience and has to be based on the first principles. As the complexity of the physical processes responsible for stability failure have increasingly made time-domain numerical simulation the main tool for stability assessment, particular emphasis is made on the development an application of such tools.

The included papers have been selected by the editorial committee and have gone through an additional review process, with at least two reviewers allocated for each. Many of the papers have been significantly updated or expanded from their original version, in order to best reflect the state of knowledge concerning stability at the time of the book’s publication.

The book consist of four parts: Mathematical Model of Ship Motions in Waves, Dynamics of Large Motions, Experimental Research and Requirements, Regulations and Operations.

Table of Contents


Mathematical Model of Ship Motions in Waves: New Simulation Tools


Chapter 1. TEMPEST—A New Computationally Efficient Dynamic Stability Prediction Tool

The US Navy has embarked upon the development of a new computational tool for simulating the responses of a ship operating in severe sea states. This new tool, TEMPEST, is designed to be computationally efficient to support real-time training simulators as well as high-resolution evaluation of surface-ship, dynamic-stability performance across a wide range of possible environmental conditions. TEMPEST aims to improve the state-of-the-art for real-time computations through the inclusion of nonlinear (body-exact) hydrodynamic perturbation forces and physics-based, viscosity-influenced lift and cross-flow drag forces. Slender-ship and low-aspect-ratio lifting-surface theories provide the ability to maintain computational efficiency while including the dominant nonlinearities within the dynamic stability problem. This paper argues for the efficacy of TEMPEST’s theory in reconciling the need for accurate predictions with computational efficiency.

William F. Belknap, Arthur M. Reed

Mathematical Model of Ship Motions in Waves: Environment


Chapter 2. Modeling of Incident Waves Near the Ship’s Hull (Application of Autoregressive Approach in Problems of Simulation of Rough Seas)

This chapter introduces the basics of the ARMA (Autoregressive Moving Average) Autoregressive/ moving average model (ARMA) model of short-crested wind wavesShort-crested waves . The model consists of an autoregressive component for temporal dependence and evolution and a two-dimensional moving average component for spatial dependence and propagation. A brief description of the validation of the model is given with special emphasis on the analysis of the dispersion relationship.

Alexander B. Degtyarev, Arthur M. Reed, Vladimir Mareev

Chapter 3. Evaluation of Hydrodynamic Pressures for Autoregressive Model of Irregular Waves

This paper proposes a new way of simulating the pressure field of the incident wave near a ship’s hull. The approach is based on an autoregressive moving average (ARMA) model of the incident wave surface. This model retains all of the hydrodynamic characteristics of sea waves and allows the accurate solution of the potential flow problem and calculation of the hydrodynamic pressures below the surface. This chapter describes the solution of two-dimensional and three-dimensional problems.

Alexander B. Degtyarev, Ivan Gankevich

Mathematical Model of Ship Motions in Waves: Consideration of Forces


Chapter 4. Application of Computing Hydrodynamic Forces and Moments on a Vessel Without Bernoulli’s Equation

Traditionally the hydrodynamic force on a ship’s hull is obtained by integrating the pressure over the hull, using Bernoulli’s equationBernoulli’s equation to compute the pressures. Due the need to evaluate $$\varPhi _t$$ , $$\varPhi _x$$ , $$\varPhi _y$$ , $$\varPhi _z$$ at every instant in time, this becomes a computational challenge when one wishes to know the hydrodynamic forcesHydrodynamic forces (and moments) on the instantaneous wetted surface of a vessel in extreme seas. A methodology that converts the integration of the pressure over the hull surface into an impulse, the time derivative of several integrals of the velocity potential over the surface of the vessel and possibly the free surface near the vessel is introduced. Some examples of applying the impulsive theory to 2- and 3-dimensional bodies are presented.

Arthur M. Reed, John G. Telste

Chapter 5. Modelling of Hull Lift and Cross Flow Drag Forces in Large Waves in a Computationally Efficient Dynamic Stability Prediction Tool

The[aut] Hughes, M. J. US Navy[aut] Kopp, P. J. is developing a new computationally efficient simulation tool to predict the responses of a ship operating in severe sea states. The tool computes the total force on the ship as the summation of component forces. An important component to the total force on the ship is the force from hull lift and cross-flow separation. These forces are predicted in calm water by maneuvering simulation tools but are often ignored by traditional seakeeping simulation tools. As viscous effects are important in the prediction of these forces, most maneuvering simulations are based on empirical data from calm water maneuvering tests. While these methods are valid in calm water the wetted shape of the hull changes significantly in large waves having significant influences on the hull lift and cross flow drag forces. In the present method a hull lift and cross flow drag force model is presented that accounts for the varying wetted geometry of the hull in waves. The method uses calm water maneuvering data from model tests and RANSCFD / RANS calculations to calibrate the model. Proper modeling of the hull lift and cross flow drag force in large waves is very important for the prediction of some dynamic stability events such as broaching and broaching leading to capsize.

Michael J. Hughes, Paul J. Kopp, Ronald W. Miller

Chapter 6. Improved Maneuvering-Based Mathematical Model for Free-Running Ship Motions in Following Waves Using High-Fidelity CFD Results and System-Identification Technique

Predicting maneuverability and stability of a free running ship in following and quartering waves are one of the most important topics to prevent broaching; however current mathematical models show quantitative errors with the experimental data while high-fidelity CFD simulations show quantitative agreement, which provides the opportunity to improve the mathematical models for free running ship dynamics in waves. In this study, both maneuvering coefficients and wave model in the mathematical model are improved utilizing system identificationSystem identification technique and CFD free running outputs. From turning circle and zigzag calm water CFD free running data, the maneuvering coefficients are estimated. The wave correction parameters are introduced to improve the wave model, which are found from a few forced and free running CFD simulations in waves. The mathematical model with the improved parameters shows much better agreement with experiments in both calm water and waves than the original mathematical model. The original mathematical model was based on the maneuvering coefficients estimated from several captive tests and wave forces calculated from linear Froude-Krylov forces and diffraction forces based on a slender ship theory.

Motoki Araki, Hamid Sadat-Hosseini, Yugo Sanada, Naoya Umeda, Frederick Stern

Mathematical Model of Ship Motions in Waves: Roll Damping


Chapter 7. Some Results from a New Time-Domain Bilge Keel Force Model

A new non-linear, time domain bilge keel force model was recently developed for inclusion in the new time-domain seakeeping/maneuvering in waves code TEMPEST, being developed by NSWCCD. This bilge keel force model combines a full unsteady extension of Bollay’s non-linear low aspect ratio lifting surface theory for cases with adequate forward speed with a more conventional approach for cases with zero or low forward speed, using Morison’s equation. This paper presents some representative results from the new bilge keel force model for a surface combatant for various roll amplitudes, roll periods, and forward speeds.

David S. Greeley

Chapter 8. Some Topics for Estimation of Bilge Keel Component of Roll Damping

In [aut] Kakinoki, T. this[aut] Yoshioka, Y. paper, two[aut] Miyamoto, S. topics of roll dampingRoll damping estimation are introduced. In these topics, bilge-keel component of roll damping is focused, because this component is generally most part of viscous roll damping. First topic is the bilge-keel component of roll damping under shallow draftShallow draft and large amplitude roll motion, and an estimation method of the draft effects based on Ikeda’s methodIkeda’s method is proposed. Second topic is the bilge-keel component of roll damping under transitional and non-periodic rolling, an estimation method for time-domain simulation based on Ikeda’s method is introduced and its estimated results are compared with measured results of roll damping in irregular forced rolling.

Toru Katayama, Yuuki Yoshioka, Takahiro Kakinoki, Shugo Miyamoto, Yoshiho Ikeda

Chapter 9. Considerations for Bilge Keel Force Models in Potential Flow Simulations of Ship Maneuvering in Waves

Requirements[aut] Brown, A. for ship operations, both naval and commercial, may result in increased exposure to heavy weather and the occurrence of large amplitude motions. In order to enable evaluation of hull form designs, or to develop detailed ship specific operator guidance for these critical conditions, potential flow sectional, or strip-theory based, approaches remain the most practical method for fast ship motions simulations. However, some essential physical effects regarding the bilge keels are not captured by potential flow sectional formulations. To examine the relative importance of these effects, a series of unsteady RANSCFD/RANS (URANS) computations were performed for the ONR Tumblehome model experiencing large amplitude roll motion at both zero and forward speed conditions, in calm water and in waves.

Christopher C. Bassler, Ronald W. Miller, Arthur M. Reed, Alan J. Brown

Chapter 10. Assessment of Ship Roll Damping Through Full Scale and Model Scale Experiments and Semi-empirical Methods

This[aut] Huss, M. paper[aut] Kuttenkeuler, J. presents[aut] Werner, S. unique[aut] Soder, C, -J. experimental set-ups in model scale and full scale for evaluating roll dampingRoll damping properties of a Panamax Pure Car and Truck Carrier at speed. The purpose of this study is to develop a method for the assessment of roll damping based on full scale trials and to validate the use of roll damping derived from model tests for full scale vessels. Experimental data are also used to assess a semi-empirical method that today provides input for the prediction of critical rolling events such as parametric rollingParametric roll and severe rolling motions in general.

Carl-Johan Söder, Anders Rosén, Sofia Werner, Mikael Huss, Jakob Kuttenkeuler

Chapter 11. Roll Damping of a Twin-Screw Vessel: Comparison of RANSE-CFD with Established Methods

A RANSE-CFDCFD / RANS method is applied to estimate the roll dampingRoll damping of a modern twin-screw RoPax vessel. The simulations are carried out in full scale and with an undisturbed water surface. The harmonic forced roll motion technique is implemented. The influence of ship speeds, the vertical position of the roll axis and roll amplitudes up to 35 $${^\circ }$$ are investigated. The interaction between the bilge keels and the ship hull is analyzed. The damping effects of further appendages are discussed. All simulation results are compared with the established method developed by Ikeda and a neural networkNeural network method based on Blume’s roll damping measurements. The established methods were developed based on studying results of single-screw ships. It can be concluded that both established methods provide acceptable results in certain ranges. For large roll amplitudes, the established methods are out of range and cannot deliver reliable results.

Sven Wassermann, Nikolai Köllisch, Moustafa Abdel-Maksoud

Mathematical Model of Ship Motions in Waves: Damaged Ship


Chapter 12. Calculation Method to Include Water on Deck Effects

Green waterGreen water is an important issue regarding ships stability as it may dramatically change the loading of the ship compared to its dry deck condition. Until now, computational methods capturing this event are very time consuming as they often try to capture the complete dynamics of the flow over the vessel’s structure and deck using CFD. Such methods are not practical when dealing with numerous lengthy time domain simulations for long term stability assessments. MARIN has developed a fast method to be implemented in its 6 DOF time domain program FREDYN. This method has as objectives to be as fast as possible, even real time if achievable, but at the same time take into account correctly the mass of water flooding on the deck during green water events. The method is based on pre-computing the steady forward speed wave pattern and diffracted and radiated waves. The steady wave is computed for a series of sailing conditions using the in-house 3D linear panel code DAWSON. The diffracted and radiated waves are pre-computed using in-house 2D strip theory potential code SHIPMO for a series of frequencies and sailing conditions. A ship generated wave is then computed at each time step during the simulation using the current position and motions of the ship. This improves the computation of a realistic wave elevation consisting of the incident, steady, diffracted and radiated waves along the hull of the ship. This wave profile is then used to feed our flooding module which computes flows in tanks, compartments and through openings. This flooding model is based on a quasi-static Bernoulli formulation and empirical discharge coefficients. It is used to compute the flow over the bulwarks and through the freeing ports to the deck.

Nicolas F. A. J. Carette, Frans van Walree

Chapter 13. Study on the Motions and Flooding Process of a Damaged Ship in Waves

To[aut] Nam, B. -W. study[aut] Sung, H. G. the motions and floodingFlooding process of a damaged cruiser, a series of experiments and numerical calculations have been performed in calm water and in waves. Two damaged scenarios are selected to investigate effect on the motions and flooding process; midship section and fore section. The results of the experiment, relating to the quasi-static numerical model and the quasi-dynamic numerical model are compared . Numerical simulations are then conducted using quasi-static and quasi-dynamic models. The quasi-dynamic model adopts the mass-spring system for internal water motion description and the model considers the dynamics of free surface as ship motion. The flooding water with free surface in midship section changed the heave and roll of the cruiser and roll RAOs in waves because the center of flood water amidships locates on the starboard side and the flooded water with large free surface area in the upper compartment generates sloshing flow. The developed quasi-dynamic model reproduces these flooding water motion in calm water and waves.

Seokkyu Cho, Honggun Sung, Sayoung Hong, Bowoo Nam, Sungchul Hwang, Youngsik Kim

Chapter 14. Numerical Study of Damaged Ship Motion in Waves

An integrated numerical method, which couples a seakeeping solver and a Navier-Stokes (NS) solver with the volume of fluid (VOF) model, has been developed to study the behavior of a damage ship in waves. The dynamics of water floodingFlooding and sloshing in the compartments were calculated by the NS solver, while the hydrodynamic forces induced by the sea wave on the external hull surface were calculated using the seakeeping solver. To validate its performance, the solver was applied to the flooding problem of a damaged Ro-Ro ferry in regular beam seas. The computed results are satisfactory in comparison with the experimental data.

Zhiliang Gao, Qiuxin Gao, Dracos Vassalos

Chapter 15. 3D GPU SPH Analysis of Coupled Sloshing and Roll Motion

The coupled roll motion response of a single degree of freedom system to which a passive anti-roll tank has been attached is considered and its performance studied numerically with a 3D GPU SPH code, aimed at simulating the sloshingSloshing flows occurring inside the tank. Results are compared with experiments from Bulian et al. (2010), in which 2D simulations were also presented. Progress achieved thereafter is documented, mainly consisting in the implementation of a parallelized solver that runs on a GPU card, which allows the simulation of low resolution 3D and high resolution 2D computations.

Luis Pérez Rojas, Jose L. Cercos Pita

Dynamics of Large Ship Motions: Parametric Roll


Chapter 16. Prediction of Parametric Rolling in Irregular Head Waves

For providing a benchmark data for numerical codes for parametric rollParametric roll prediction, a model experiment of a post-Panamax C11 class containership whose hull form is slightly modified from its original but opened for public was conducted and significant parametric rolling in irregular head waves was recorded. A 3DOF (degrees of freedom) numerical model based on the nonlinear strip theory is developed. The numerical code for time domain simulations is developed for the prediction of large amplitude of parametric roll both in regular and irregular head waves. Comparisons between the model experiment and the numerical simulations show good agreement under the consideration of dispersion due to practical non-ergodicityPractical non-ergodicity . By utilizing the developed numerical model, it was demonstrated that small height of the bilge keels is a major reason why significant parametric roll could happen for a C11 class post-Panamax containership in 1998.

Hirotada Hashimoto, Naoya Umeda

Chapter 17. Investigation on Parametrically Excited Motions of Spar Platforms in Waves

As offshoreOffshore installation oil exploration goes into deeper waters, spar platforms appear as a good alternative for oil field developments due to their inherent hydrodynamic behaviour regarding its vertical motions response in waves. Spar’s long natural periods in heave and pitch guarantee the good linear responses of the associated motions; however, nonlinear unstable motions can be triggered. Many numerical and experimental investigations have put forward the reasoning that this kind of floating structure is prone to parametrically induced motions due to changes in their pure hydrostatic restoring. Based on an analytical model, the present paper demonstrates that the main contribution to parametric excitation comes from variations in the pressure field associated to the incident wave and not from purely nonlinear hydrostatic actions. A nonlinear mathematical model based on Taylor series expansions, Neves[aut] Neves, M. A. S. and Rodríguez (Ocean Eng 33(14):1853–1883, 2006) [aut] Rodríguez, C. A. , is employed to explain the underlying mechanism that leads to the phenomenon of Mathieu instabilityMathieu instability in vertical deep drafted cylinders. Analytical expressions are derived for the nonlinear hydrostatic and Froude-Krilov actions. A set of coupled time-dependent equations is obtained. Based on that, general conditions for the appearance of principal resonances are derived. These analytical results are verified by means of numerical simulations. Numerical analyses are carried out for regular wave conditions and a domain of parametric amplifications is obtained.

Claudio A. Rodríguez, Marcelo A. S. Neves

Chapter 18. A Study on Unstable Motions of a Tension Leg Platform in Close Proximity to a Large FPSO

The[aut] Esperança P. T. T present[aut] Rivera, L. A. paper elaborates on model experimental results obtained from tests conducted with a TLP connected to a nearby positioned FPSO. The tests revealed, at a given range of wave periods, the onset of unexpected large oscillatory yaw motions of the platform whereas the FPSO remained rather stable when the TLP was directly excited in sway. The paper summarizes the model experiments emphasizing the types of coupled motions taking place. It is observed that as the yaw motion develops increasing amplitudes the sway motion is reduced, pointing out to an interesting exchange of energy between the sway and yaw modes. A mathematical model is proposed to describe the main aspects of the two-body moored system. In principle a 12 DOF model is contemplated. Numerical simulations are compared to the time series obtained from the experiments showing adequate agreement.

Luis Alberto Rivera, Marcelo A. S. Neves, Roberto E. Cruz, Paulo de Tarso T. Esperança

Dynamics of Large Ship Motions: Surf-riding


Chapter 19. Bifurcation Analysis of Ship Motions in Steep Quartering Seas, Including Hydrodynamic “Memory”

Steady-state ship dynamics in steep harmonic waves encountering the ship from stern quartering direction is under investigation. Bifurcation analysis is performed by applying a numerical continuation methodContinuation method . Stationary as well as periodic states are traced, as selected control parameters are varied. Regions with coexistence of different ship responses are identified. The main novelty of the paper lies in the extension of the continuation analysis to a 6-DOF model, for a quartering sea environment, with inclusion of memory effects within a potential flow framework. Complete, vessel-specific stability diagrams, for horizontal plane motions, are produced in an automated and time-efficient manner. These could provide useful guidance to ship masters for avoiding the occurrence of surf-ridingSurf-riding and broaching-toBroaching-to .

Ioannis Tigkas, Kostas J. Spyrou

Chapter 20. Modeling of Surf-Riding in Irregular Waves

Surf-ridingSurf-riding is an important phenomenon for the evaluation of ship dynamic stability, as it is related to one of the principal mechanisms of broaching-to. The evaluation of the probability of surf-riding in irregular wavesIrregular waves is a necessary step toward determining the probability of broaching-to following surf-riding. To facilitate the probabilistic study of surf-ridingSurf-riding , a simple model of surging and surf-riding in irregular waves of variable bandwidth is introduced. This model can be used to identify patterns of surf-riding in irregular waves.

Vadim L. Belenky, Kostas J. Spyrou, Kenneth M. Weems

Chapter 21. Definitions of Celerity for Investigating Surf-Riding in an Irregular Seaway

As is well-known, if the speed of a ship operating in high, fairly regular, following waves exceeds wave celerityCelerity , then surf-ridingSurf-riding is realized. This motivates one to approach the calculation of the probability of surf-riding in irregular seas as a threshold exceedance problem. However, it is unknown whether such a simple phenomenological rule, using the celerity as threshold, could also be applicable for the ship dynamics associated with a stochastic wave environment. To clarify this, a suitable definition of wave celerity for an irregular seaway needs first to become available. In this chapter, we define celerity as the velocity of propagation of a fixed slope value of the wave profile. This leads to the concept of instantaneous celerity, opening up a window to the literature of instantaneous frequency in signal processing. As it turns out, instantaneous celerity is not always a consistently smooth and bounded curve. Other definitions of local celerity are also conceivable. We tested a few different selections, obtaining time-dependent celerity curves for various types of waves. Relaxing the requirement for a narrow-band spectrum, we offer some clues about the effect of spectrum’s bandwidth on celerity. In a further step, simultaneous treatment of the “wave” and “ship” processes is implemented, in order to investigate the potential of applying a local celerity condition for surf-riding’s prediction. Various patterns of ship motion, before and into surf-riding, are observed.

Kostas J. Spyrou, Vadim L. Belenky, Nikos Themelis, Kenneth M. Weems

Dynamics of Large Ship Motions: Stochastic Treatments


Chapter 22. Estimating Dynamic Stability Event Probabilities from Simulation and Wave Modeling Methods

Predicting the dynamic stability of ships in severe wave environments is challenging, not only due to the complex non-linear hydrodynamics, but also the need to characterize the rarity of events. The latter involves conducting enough simulations to calculate associated small probabilities or alternate approaches for estimating the rarity of events. This paper presents techniques for calculating probabilities of occurrence of rare dynamic stability events using direct counting, Poisson distribution fitting techniques and estimating the dynamic event probabilities. The latter probability estimate is obtained by defining dangerous wave conditions that produce rare events through hydrodynamic simulations and estimating their probabilities of occurrence through joint probability distributions or simulations of the wave environment. The accuracy of these calculations is discussed. An example application is presented using a U.S. Coast Guard Cutter along with information useful for operator guidance in heavy weather. A recommendation is presented for further work on defining the limiting probabilities one might use for design or operational criteria.

M. Ross Leadbetter, Igor Rychlik, Karl Stambaugh

Chapter 23. Stochastic Wave Inputs for Extreme Roll in Near Head Seas

An approach to generate the extreme value distribution of parametric rollParametric roll in near head sea conditions is presented using a Design Load Generator (DLG) Design Load Generation (DLG) , a process to approximate the extreme value distribution of a Gaussian random variable. Statistics of the roll amplitudes of a Joint High Speed Sealift (JHSS) concept hull calculated from the DLG and the Large Amplitude Motion Program (LAMP) are compared in Weibull space with the results from limited Monte Carlo simulations. The interpretation of the exposure period of the DLG results is included.

Dae-Hyun Kim, Armin W. Troesch

Chapter 24. Critical Wave Groups Versus Direct Monte-Carlo Simulations for Typical Stability Failure Modes of a Container Ship

In the second Generation Intact Stability Criteria currently developed at IMO, the process of direct stability assessment (DSA) and providing operational guidance (OG) are interlaced with a requirement of performing a large number of numerical simulationsNumerical simulation tool (FREDYN, LAMP, OU-PR, PANSHIP, PROTEUS, ROLLS, SNU-PARAROLL,TEMPEST, WISH) . However, extreme roll motions that are generally behind stability failures are rare events as any extreme responses. An additional significant difficulty is that roll response as stochastic process is usually non-Gaussian, therefore, close-form expressions for the probability of extreme roll responses, based on spectral moments, are in general not applicable. A practical approach proposed recently exploits the idea that extreme events occur due to the encountering of extreme wave groups (critical wave episodes). This could alleviate the need for a large number of simulations by focusing on the systematic identification of those deterministic wave sequences that generate unacceptable roll responses. Taking a first step towards a systematic validation process of the wave groups methodWave groups method , the present study compares the exceedance probabilities of 40° roll angle and of g/2 lateral acceleration, computed by the critical wave groups method with Monte-Carlo simulations for a large containership. The nonlinear seakeeping code rolls is used as mathematical model of ship motion. Typical loading conditions where various stability failure modes can occur are examined.

Vladimir Shigunov, Nikos Themelis, Kostas J. Spyrou

Chapter 25. Solving the Problem of Nonlinear Ship Roll Motion Using Stochastic Dynamics

Due to nonlinear viscous damping and the softening characteristic of the stiffness, the roll motion of a ship exhibits complex dynamics. Specifically predicting the probabilistic characteristics of roll response in an irregular seaway is still a challenging problem and continues to be of interest for both practitioners and researchers. In this work two techniques from the theory of stochastic dynamics are applied to study the probabilistic nature of roll motion in irregular seas. The first method is the “Moment Equation method” where the roll response moment equation is formulated from a six dimensional state space rolling model with a fourth order linear filter using the Itô differential rule. The resulting moment equations are solved using a cumulant neglect technique. Alternatively in the second approach, the probability density function of the rolling response is evaluated by solving the corresponding Fokker Planck Equation of the system using “Path Integral method”.

Jeffrey M. Falzarano, Zhiyong Su, Arada Jamnongpipatkul, Abhilash Somayajula

Chapter 26. The Capsize Band Concept Revisited

A[aut] Tsakalakis, N. concept for analytical representation of the capsize rate, a measure directly related to damage ship survivability, has attracted attention ever since the first attempts were made to explain the behaviour of a damaged ship in waves. Attempts in the late 1990s helped to enhance understanding and facilitate characterisation of phenomena pertaining to capsize probability and time to capsize in given environments and loading conditions, but a consistent verifiable formulation is still lacking. In this respect, pursuing an analytical approach to express the capsize rate offers many advantages, time efficiency being amongst the most important. In an era when stability/survivability calculations are required to be carried out in real time, there is a need for a model accounting for the random nature of capsize whilst achieving accuracy close to that of time-domain simulations with simple hydrostatic calculations. This study is an attempt to establish a new methodology for survivability assessment by means of a multivariable analytical model based on numerical simulations, validated against the results of physical model tests.

Nikolaos Tsakalakis, Jakub Cichowicz, Dracos Vassalos

Chapter 27. Dependence of Roll and Roll Rate in Nonlinear Ship Motions in Following and Stern Quartering Seas

The changing stabilityFollowing and stern quartering seas of a ship in waves may have a significant influence on the probabilistic properties of roll in irregular following and quartering seas. In particular, nonlinear effects may lead to dependenceDependence and correlation between roll angles and rates, which will have significant repercussions on the application of the theory of upcrossings for evaluating the probability of a stability failure related to roll motion such as capsizing. The roll response of a ship in a stationary seaway is a stationary stochastic process. For such a process, the roll angle and its first derivative are, by definition, not correlated and are often assumed to be independent. However, this independence can only be assumed a priori for normal processes, and the nonlinearity of large-amplitude roll motions can lead to a deviation from normal distribution. In the present work, the independence of roll angles and rates is studied from the results of numerical simulationsNumerical simulation tool (FREDYN, LAMP, OU-PR, PANSHIP, PROTEUS, ROLLS, SNU-PARAROLL,TEMPEST, WISH) from the Large Amplitude Motion Program (LAMP), which includes a general body-nonlinear calculation of the Froude-Krylov and hydrostatic restoring forces. These simulations show that, for the considered case, roll and roll rate are independent in beam seasBeam seas , even though the distribution of the roll response is not normal. However, roll angles and roll rates for stern quartering seas are not independent.

Vadim L. Belenky, Kenneth M. Weems

Experimental Research: Techniques


Chapter 28. Regular Wave Testing as a Crucial First Step for Dynamic Stability Evaluation

The[aut] Dipper, M. J. DDG51 pre-contract hull form as represented by Model 5514 was evaluated for capsize events at End of Service Life Load Limit for the Righting Arm Limiting and Intact 100 Knot Wind Limiting KG Conditions. The hull was evaluated using a matrix of various following sea headings and Froude numbers at various regular wave lengths and steepness. The results provide a good comparison point to computer simulations and a way to verify regimes of concern relating to dynamic stability. The domains of reduced dynamic stability can be used to determine future areas of study for random or deterministic irregular wave testing. The model test also provides data to compare measured roll decay and maneuvering characteristics against simulation predictions for validation. Experimental techniques and model layout are described. Suggestions for future improvements in regular wave testing are provided. Even though regular wave dynamic stability testing provides a basic evaluation of dynamic stability, the results can be used as a key starting point for additional testing or as a basis for operational guidance.

David D. Hayden, Richard C. Bishop, Martin J. Dipper

Chapter 29. An Experimental Study on Characteristics of Rolling in Head Waves for a Vessel with Nonlinear GZ-curve

InMiyamoto, S. this study, the characteristics of rolling in head waves for a vessel with strong nonlinear GZ-curve, which includes parametric rollingParametric roll , are investigated. Rolling is measured for systematically changed wave length and height under the same forward speed, which is service speed in heavy weather. As a result, the range of Te/Tϕ (Te and Tϕ are encounter wave period and the roll natural period of the model) when oscillatory rolling occurs is wider than that of previous results by Taguchi et al. (Model Experiment on Parametric Rolling of a Post-Panamax Containership in Head Waves. Proceedings of the Ninth International Conference on Stability of Ships and Ocean Vehicles, 2006), and the range spreads out wide area of Te/Tϕ > 0.5. Especially, in the range of Te/Tϕ > 0.5, oscillatory rolling is caused by large wave height and roll amplitude becomes larger than that at Te/T = 0.5. It is supposed that the result is caused by change of roll natural period caused by nonlinear GZ-curve. In order to confirm it, numerical simulations are carried out for several variations of GZ-curve. Additionally, roll measurements in irregular waves with Pierson-Moskowitz spectrum are also carried out.

Toru Katayama, Shugo Miyamoto, Hirotada Hashimoto, Yoshifumi Tai

Chapter 30. Experimental Ship Dynamic Stability Assessment Using Wave Groups

TheMelendez, M. assessment of ship performance in heavy weather, particularly dynamic stability performance, is an important but difficult assessment to make. Traditional experimental assessment methods using regular and random waves provide insight into dynamic stability performance, but may not identify, or provide a means to mitigate, specific modes of dynamic stability failure. Assessment using deterministic wave groupsWave groups method may provide repeatability and systematic exposure important for the assessment of ship designs, as well as aid in development and validation of numerical simulation tools. The deterministic grouped wave approach, when used to define ship behavior in heavy weather, can also be useful in the development of ship-specific operator guidance.

Christopher C. Bassler, Martin J. Dipper, Mark Melendez

Chapter 31. Dynamic Transverse Stability for High Speed Craft

Even in calm water, high-speed vessels can display unstable behaviors, such as chine-walking, sudden large heel, and porpoising. Large heel results from the loss of transverse stability due to high forward speed. When a planing craft begins to plane, the hydrodynamic lift forces raise the hull out of the water, reducing the underwater submergence. The available righting moment due to the hydrostatic buoyancy is, therefore, reduced. As the righting moment due to hydrostatic buoyancy is reduced, the righting moment due to hydrodynamic effects becomes important. These hydrodynamic righting effects are related to the hydrodynamic lift. This paper explores the relationship between the hydrostatic righting moment, the hydrodynamic righting moment, and the total roll restoring moment of a planing craft operating at planing speeds. A series of tow tests using a prismatic hull with a constant deadrise of $$20^{\circ }$$ measured the righting moment at various angles of heel and at various model velocities. The model was completely constrained in heave, pitch, sway, roll, yaw, and surge. The underwater volume is determined from the known hull configuration and underwater photography of the keel and chine wetted lengths. The results presented include the total righting moment with the hydrostatic and hydrodynamic contributions for various model speeds at two model displacements.

Carolyn Q. Judge

Chapter 32. Experiments on a Floating Body Subjected to Forced Oscillation in Calm Water at the Presence of an Open-to-Sea Compartment

This paper presents results of the physical experiments carried out at the SSRC, aiming at measurements of hydrodynamic reactions on a cylindrical body forced to roll in calm water with an open-to-sea compartment. The research addresses the problem of ship-floodwater interactionShip-floodwater interaction —an issue of fundamental importance in predicting roll damping for ships in damaged condition.

Jakub Cichowicz, Dracos Vassalos, Andrzej Jasionowski

Experimental Research: Techniques: Validation and Benchmarking


Chapter 33. Model Characteristics and Validation Approach for a Simulation Tool Supporting Direct Stability Assessment

Significant challenges exist in the validation and formal acceptance of dynamic stability simulation tools, which can have a limiting effect on operations or concept design due to a need for conservatism. These challenges primarily consist of validation metrics and criteria, uncertainty characterization, and defining the scope of conditions (both environmental and operating) that must be examined in order to ensure that the simulation tool is valid for all conditions of interest. In discussing these challenges, this paper proposes approaches to the problem of validationValidation and formal acceptance that can be applied in future efforts.

Arthur M. Reed, William F. Belknap, Timothy C. Smith, Bradley L. Campbell

Chapter 34. Validation Approach for Statistical Extrapolation

Statistical extrapolationExtrapolation is the estimation of rare, extreme responses from data sets that consist primarily, if not entirely, of lower (non-rare) values. The validationValidation of statistical extrapolation involves elements common to all validation efforts with the additional difficulty of needing to determine the true value and its uncertainty. The determination of the true value requires an extensive amount of data in order to observe multiple rare events. In some cases, the desired extreme events may be so rare that validation is forced to accept a less rare event such as a lower threshold value. This paper reviews the basics of simulation validation and focuses on the challenges of the validation of statistical extrapolation.

Timothy C. Smith

Chapter 35. Total Stability Failure Probability of a Ship in Beam Wind and Waves: Model Experiment and Numerical Simulation

To[aut] Izawa, S. establish[aut] Matsuda, A. second-generation intact stability criteria, the International Maritime Organization requires experimentally validated numerical simulation models for stability under the dead ship condition. Here, a beam wind and wave condition is selected as the worst-case scenario and the total-stability-failure probability is quantified. The authors developed a coupled sway–heave–roll–pitch numerical model and compared it with physical experiments of a ship model in artificial irregular beam waves and fluctuating beam wind. The results indicate that the probability of total stability failure estimated by the simulation exists within the confidence interval range of those estimated by the experiment.

Takumi Kubo, Naoya Umeda, Satoshi Izawa, Akihiko Matsuda

Chapter 36. Deterministic Validation of a Time Domain Panel Code for Parametric Roll

ValidationValidation of simulation methods for dynamic stability is hampered by the fact that dynamic stability phenomena can be quite rare. In order to obtain sufficient statistical confidence in both experimental data and simulation results long duration time histories are required for a range of operational conditions. This is at most times not feasible from a practical point of view. One way of validating time domain simulation methods for dynamic stability phenomena is by deterministic validation. This means that the simulation is run in the same wave sequence as used during the model experiments. Ideally, a one to one comparison between experiments and simulations is then possible. A difficulty in such an approach is, in case of irregular waves, the reconstruction of the experimental wave train in the simulation tool. Even if this were successful, the encountered wave train in the simulations will deviate from the experimental one because it is inevitable that the position in the horizontal plane will differ from the experimental one after some time. The paper describes the deterministic validation of a non-linear, 6-DoF time domain panel code for parametric roll. The paper explains the method for reconstructing the experimental wave train in the simulation method and how to circumvent the problem of the deviation in horizontal position. Finally, comparisons between experimental and simulated time traces are given for the motions in the vertical plane.

Frans van Walree, Pepijn de Jong

Chapter 37. 26th ITTC Parametric Roll Benchmark Study

The 26th ITTCReed, A. M. Specialist Committee on Stability in Waves was assigned the task of conducting a benchmark of numerical simulation methods for the prediction of the parametric rolling of ships in head seas. The vessel chosen for the benchmark and the organizations which participated in the benchmark and their simulation tools are described. The results of the benchmark are presented.

Arthur M. Reed

Chapter 38. An Approach to the Validation of Ship Flooding Simulation Models

A[aut] Turner, T. methodology has been developed to validate a Ship FloodingFlooding simulation tool. The approach is to initially validate the flooding model and the vessel model separately and then couple the two models together for the final step in the validationValidation process. A series of model tests have been undertaken and data obtained has been utilised as part of the validation process. Uncertainty in the model test measurements and the geometry of the physical model play a crucial role in the validation process. Therefore, an important element is an assessment of the uncertainties that play a role in this process together with how they propagate and eventually influence the end result. The aim was to develop a practical engineering approach trying to use the data that was available and making educated guesses where it could not be avoided. It is by no means intended to be a full-fledged theoretical elaboration on uncertainty propagation. This paper provides an overview of the methodology adopted for the validation of the ship flooding simulation tool and presents some of the preliminary results from this study.

Egbert L. Ypma, Terry Turner

Requirements and Operation: Developments in Intact Stability Regulations


Chapter 39. Research Towards Goal Based Standards for Container Shipping

AnalysisGoal-Based Standards (GBS) and[aut] El Moctar, O. verification of rule-related technical aspects of safe and efficient container shipping are an important part of R&D activities of classification societies. Casualty statistics show that container loss in heavy weather is an important issue for innovative container ship designs. The paper demonstrates two examples of research activities aiming at the reduction of cargo losses. One example is ship-specific operational guidance, assisting the ship master to avoid excessive motions and accelerations in heavy weather. The design accelerations underlying the operational guidance are part of classification rules, requiring understanding of the physics of dynamic loads on containers and lashing. The status of the ongoing research in this area is shown, in particular, the study of the effects of container flexibility and dynamic load amplification, not addressed explicitly in the present classification rules.

Vladimir Shigunov, Helge Rathje, Ould El Moctar

Chapter 40. On Regulatory Framework of Direct Stability Assessment

Direct[aut] Peters W. S. assessment of stability, including model tests and numerical simulations, is the ultimate way to evaluate the risk of stability failure for an unconventional vessel. That is why direct assessment is considered to be the highest tier of the second generationSecond generation IMO intact stability criteria of intact-stability criteria, that are being developed by IMO. Direct assessment procedures for stability failure are intended to employ the most advanced state-of-the art technology available, yet be sufficiently practical so as to be uniformly applied, verified, validated, and approved using currently available infrastructure. This paper addresses several principal issues related to the application of numerical simulation in the IMO regulatory framework, including possible requirements for a method that adequately replicates ship motions in waves, validation of such a method, actual assessment procedures and their validation.

William S. Peters, Vadim L. Belenky, Arthur M. Reed

Chapter 41. A Probabilistic Analysis of Stability Regulations for River-Sea Ships

The present contribution focuses on the recent developments in the field of stability regulations for the river-sea shipsRiver-sea ships in Europe. The river-sea ships are primarily inland vessels that operate on the coastal sea routes on a regular basis. Due to their particular service and design, the river-sea ships may be subject to special stability requirements that incorporate seakeeping considerations to an extent. In the present analysis, some of the existing stability rules (Russian River Register) and working proposals of regulations (UNECE Resolution No. 61) intended for the river-sea ships are evaluated from the probabilistic point of view. It is demonstrated that, in some cases, these regulations are insufficient and not strict enough. Critical analysis is followed by some guidelines for possible improvement of regulations and development of new intact stability criteria for river-sea ships.

Igor Bačkalov

Requirements and Operation: Developments in Damage Stability Regulations


Chapter 42. Issues Related to Damage Stability

This chapter attempts to provide a brief historical overview of how the demands for increased safety, in combination with advances in computing hardware and software, have resulted in changes to the regulatory framework governing damage stability.

Andrew Scott

Chapter 43. Damage Stability Making Sense

Although aviation, nuclear, processing, etc. industries have long ago adopted and established preventative frameworks and procedures to safeguard against unwanted outcomes of daily operations, the maritime industry still places the emphasis on the mitigation of consequences following an accident. Despite the widely expressed opinion that prevention is the way forward, curing occupies a central position not only in every day practice but in the underlying regulatory framework as well. Contrary to this approach, the work presented here aims to create the necessary momentum towards rationalisation of the fundamental choices made during the design process, thus attracting attention to areas where prevention strategies can find fertile ground and be fruitful and cost-effective. The methodology addresses the occurrence of a collision event and the crashworthinessCrashworthiness capacity of a ship as prerequisites for its survivability assessment, with promising results to encourage further development.

George Mermiris, Dracos Vassalos

Chapter 44. Coupling of Progressive Structural Failure and Loss of Stability in the Safe Return to Port Framework

This[aut] Mermiris G. paper addresses the survivability assessment of damaged ships with respect to the coupled effects of structural degradation and damage stabilityDamage stability regulations in the context of the Safe Return to Port (SRtP)Safe return to port framework for passenger ship safety. The survivability is evaluated in the time domain with varying wave loads. The proposed methodology is demonstrated through application to two diverse but safety-critical ship types, namely a RoPax with side damage, and an Aframax tanker with asymmetric damage at the bottom.

Seungmin Kwon, Qi Chen, George Mermiris, Dracos Vassalos

Chapter 45. Impact of Watertight Door Regulations on Ship Survivability

When[aut] Person, J. demonstrating compliance with the International Convention for the Safety of Life at Sea (SOLAS), Chapter II-1 subdivision and damage stability regulationsDamage stability regulations , it is assumed that all watertight doorsWatertight door are closed and the related internal watertight subdivision is 100% effective. Unfortunately, casualty history indicates that this is not always the case. Contributing to this situation are provisions in the SOLAS regulations that permit some watertight doors to remain open or be open for extended periods of time during navigation under certain conditions. This paper provides background information on the SOLAS requirements for watertight doors and discusses whether this regulatory treatment is still appropriate for passenger ships of the future. Originally written in June 2011, an update is included to indicate the latest SOLAS regulatory developments as of June 2017.

James Person

Chapter 46. Damage Stability of Passenger Ships—Notions and Truths

A painstaking evolutionary development on damage stability of ships is giving way to unprecedented scientific and technological developments that has raised understanding on the subject as well as the capability to respond to the most demanding societal expectations on the safety of human life and to do so cost-effectively. Within less than half a century, damage stability calculations catapulted from one scenario per newbuilding (QE II, mid-1960s over a few months) to tens of thousands of scenarios (modern cruise liners in 2010s in a few weeks). Given the steepness of the learning curve and the pace of developments, it is understandable that certain notions were accepted as truths without due rigor and, as such, continue to shape contemporary thinking and developments. This paper draws attention to various issues that are emerging as knowledge grows and proposes a way forward for establishing a stronger foundation to safety assurance in the maritime sector and for future developments on the subject.

Dracos Vassalos

Chapter 47. Defining Rational Damage Stability Requirements

The[aut] Konovessis, D. major benefit of switching from the deterministic frameworks for damage stabilityDamage stability regulations of the past to the current performance-based state of the art is the ability to have a measurement of the level of survivability of any given design. The required level of survivability is probably the key parameter in any probabilistic framework, in essence answering the question “how safe is safe enough?”. To this end, survivability analysis results on representative cruise and Ro-Pax ships can be related to design and operational parameters with a view to define and quantify the relationships between damage survivability characteristics following a collision and time available for evacuationEvacuation with potential outcomes in terms of people potentially at risk. For this paper, established numerical methods for the measurement of performance-based survivability have been utilised and used as benchmark against available analytical methods in an attempt to define a rational requirement for the level of survivability.

Nikolaos Tsakalakis, Dimitris Konovessis, Dracos Vassalos

Requirements and Operation: Design, Planning and Onboard Guidance


Chapter 48. Design Requirements for Stability and Minimal Motions in a Storm

The hydrodynamics of a ship in a storm is not limited to the hull below the calm-water waterline. In a storm, the operating waterline varies between the bilge and the deck, causing unpredictable wave forces on the hull as well as the possibility of slamming on flat surfaces and the flared sections of the vessel. The present work describes the early stage of a designDesign for storm seaworthness process for a hull form that accounts for the range of changing of the waterline in order to insure stability under severe heave. With this approach, it is possible to reduce the metacentric height, which minimizes roll resonance. The concept is part of a consistent ship design process; conventional naval architectural approaches will still be needed for successful solutions for reducing the pitching and yawing of the vessel and as a necessary condition for using active stabilizers and other seaworthiness improvements.

Vasily N. Khramushin

Chapter 49. Further Perspectives on Operator Guidance and Training for Heavy Weather Ship Handling

Historically[aut] Van Buskirk L. J. , mariners have received minimal formal training in heavy weather shiphandling, relying on mentoring and hands on experience to develop shiphandling skills for dangerous environmental conditions. Maritime organizations are increasingly turning to technology to reduce the inherent risks of heavy weather, including operator guidanceOperator guidance systems and simulation to train watch personnel. Shiphandling simulators are on the cusp of extending training capabilities from simple maneuvering situations to highly realistic heavy weather scenarios, resulting in vastly improved training effectiveness. This is especially critical as actual time spent afloat may represent proportionately less of a mariner’s total career.

Laurie J. Van Buskirk, Philip R. Alman, James J. McTigue

Chapter 50. Onboard Analysis of Ship Stability Based on Time-Varying Autoregressive Modeling Procedure

In[aut] Matsuda, A. this study, it is clarified that a dynamical system of rolling motion can be approximated by a time-varying autoregressive modelAutoregressive / moving average model (ARMA) , which is a kind of statistical model. As the result, when it is possible to measure the time series of rolling motion, a ship’s stability can be judged based on time series analysis by using a time-varying autoregressive modeling procedure. As for the verification of this method, the results of the model experiment for parametric roll resonance were used. It was confirmed that an evaluation of ship safety is possible based on the proposed procedure.

Daisuke Terada, Akihiko Matsuda

Chapter 51. FLO/FLO Heavy Lift Critical Stability Phases

The[aut] Bruhns, H. US Navy[aut] Handler, P. has [aut] Jarecki, V. used FLO/FLO heavy lift transport as an alternative to towing for the transport of damaged vessels as well as transport of smaller vessels not suited for ocean transit. There are critical stability considerations that have to be assessed prior to conducting a heavy lift operationHeavy lift operation , specifically “Draft at Instability” and “Minimum Stability”. During de-ballasting of the heavy lift ship with the lifted vessel on the docking blocks, the reaction of the docking blocks on the lifted vessel is effectively the same as removing weight from the lifted vessel’s keel (similar to what occurs when a floating dry-dock is de-ballasted). This raises the lifted vessel’s centre of gravity thus reducing the lifted vessel’s metacentric height (GM) until the lifted vessel’s GM is zero. During a critical part of the FLO/FLO heavy lift operation the cargo deck of the FLO/FLO heavy lift ship will be completely submerged. During this phase, only the water-plane of the hull structure which extends above the cargo deck will provide stability for the heavy lift ship. The heavy lift ship will pass through a phase of “Minimum Stability”, which should not occur at the same time that the lifted vessel assumes its “Draft at Instability”. The lifted vessel and the heavy lift ship may roll out of phase, causing landing problems, or causing the lifted vessel and/or the FLO/FLO heavy lift ship to become unstable, assume a large list or even capsize. Computer naval architectural software programs HECSALV and POSSE are effective tools in modelling critical stability phases for FLO/FLO heavy lift operations. This paper discusses the critical stability phases of a FLO/FLO heavy lift operation, and the methods and practices to plan for and mitigate the effects of reduced stability at these phases.

Paul Handler, Vincent Jarecki, Hendrik Bruhns

Requirements and Operation: Stability of Naval Vessels


Chapter 52. Developing a Shared Vision for Naval Stability Assessment

The design and operating philosophy for naval vessels is driven by necessity of strategic capability, including the capability to deploy at any time to any location. A key enabler for this capability is the hydrodynamic stability of the vessel. The Naval Stability Standards Working Group, in conjunction with the Co-operative Research Navies Dynamic Stability Project, have been working to develop a clear understanding of the limitations and range of applicability of stability criteria and methods of assessing dynamic stability. They have investigated the relationship between GZ and form parameters and the probability of capsize, and have performed studies into the nature of the control variables used and the collinearity of the ship specific assessment parameters. This work will lead to a set of rational criteria for the stability of naval frigates, with a future expansion of the methods to other types of naval platforms.

Douglas Perrault, Steve Marshall

Chapter 53. Approaches for Evaluating Dynamic Stability in Design

There are many ways of treating dynamic stability. No single approach is always best, but must be defined relative to each design and each yields a fidelity proportionate to resources and technological maturity. During the ship design process choices must be made that balance the approach within a wide trade space encompassing ship design characteristics, operational doctrine, technical risk managementRisk management , operational safety, cost and schedule. Existing static approaches do not directly account for ship dynamics. There is a clear need to develop a framework for integration of technical approaches into the ship design/acquisition process. The objective of this paper is to define a basis for outlining the range of intact dynamic stability methodologies that can be employed to naval ship design that address dynamic stability in such a way as to minimize technical and safety risks in an economical manner. The paper summarizes ongoing work by the Naval Stability StandardsNaval stability standards Working Group (NSSWG), and outlines relevant technical approaches suitable for employment on naval ship designs from preliminary/concept design stages through to operator guidance.

Philip R. Alman

Chapter 54. Tolerable Capsize Risk of a Naval Vessel

Many[aut] Peters, A. of the operations and duties conducted by naval ships involve a degree of risk. This risk is somewhat unavoidable due to the nature of operating a warship at sea, where operational requirements can put the vessel and crew in harms way. One of the hazards that the crew is subjected to while on operations is that of the weather. The objective of this chapter is to discuss the tolerable riskTolerable risk associated with the loss of a naval vessel due to the weather conditions. A review of tolerable risk and potential methodologies of calculating an annual probability of loss of the vessel which uses time domain simulations and statistics of observed weather conditions aboard naval ships are presented.

Andrew J. Peters

Chapter 55. Thoughts on Integrating Stability into Risk Based Methods for Naval Ship Design

Design for Safety (DFS), Goal Based Standards (GBS)Goal-Based Standards (GBS) and Formal Safety Assessment (FSA)Formal Safety Assessment (FSA) are powerful tools which establish a framework for integrating stability into a risk based design process. They provide a foundation for the development of novel designs which can provide insight that is not attainable through any other means. Naval ships are complex systems, sometimes operating in an environment defined by risk acceptance and risk taking beyond those of their commercial counterparts. The hazards seen by a naval ship in its service life may not be foreseen during design. The development of a design for safety process for naval ships should be capable of reflecting the nature of the military mission. Concurrently, there is certain fidelity inherent in the process that should be carefully defined. Three cases to categorize the risk assessment ‘fidelity’ are defined and discussed. These highlight the dangers of overstating and understating risk. Lastly the challenges of defining intact and damage stability risk in light of the sensitivity to the state of knowledge for naval ships are discussed.

Philip R. Alman


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