Stability assessment for intact ships in the light of model experiments

A systematic method for assessing intact ship stability with a free-running model in a seakeeping and maneuvering basin is proposed in this paper. Model experiments were carried out in extremely steep regular waves for a model drifting, running in head seas, and quartering seas. This method was applied to two purse seiners, and efficiently identified thresholds in metacentric heights for capsizing of these ships. These capsizing thresholds are compared with requirements of the IMO Code on Intact Stability. This series of model experiments also confirms that capsizing at the threshold occurs only in quartering seas, and shows that capsizing is caused by broaching, loss of stability on a wave crest, or bow diving. Received for publication on Jan. 20, 1999; accepted on July 6, 1999     

Nonlinear dynamics of ship capsizing due to broaching in following and quartering seas

To provide a theoretical methodology to predict the critical condition for capsizing due to broaching, a nonlinear dynamical system approach was applied to the surge–sway–yaw–roll motion of a ship running with an autopilot in following and quartering seas. Fixed points of a mathematical model for the ship motion and unstable manifolds of the fixed point near the wave crest were systematically investigated. As a result, the existence of heteroclinic bifurcation was identified. With numerical experiments, it was confirmed that this heteroclinic bifurcation reasonably well represents the critical condition for capsizing due to broaching. Thus the nonlinear dynamical approach can be substituted for tedious numerical experiments. Received for publication on Nov. 20, 1998; accepted on March 16, 1999     

Broaching prediction of a wave-piercing tumblehome vessel with twin screws and twin rudders

The new intact stability criteria which are under development at the International Maritime Organization (IMO) are required to cover a broaching phenomenon, well known as a great threat to high-speed vessels which can lead to capsizing. Some reports exist which demonstrate that their numerical models can predict a highly nonlinear phenomenon of broaching. However, additional validation studies are needed for unconventional vessels, in addition to conventional ones, to develop direct stability assessment methods for the new intact stability criteria. In this research, we selected as the subject ship a wave-piercing tumblehome vessel with twin screws and twin rudders, a design expected to be one of a new generation of high-speed monohull ships. Firstly, a series of captive model tests were conducted to measure the resistance, the manoeuvring forces, the wave-exciting forces, the heel-induced hydrodynamic forces, and the roll restoring variation for the unconventional tumblehome vessel. Secondly, the existing mathematical model which had been developed for broaching prediction of conventional vessels with a single propeller and a single rudder was extended to unconventional vessels with twin propellers and twin rudders. Finally, comparisons between numerical simulations and the existing free running model experiments were conducted. As a result, it was demonstrated that fair quantitative prediction of broaching is realised when the rudder force variation, the roll restoring variation and the heel-induced hydrodynamic force for large heel angles are taken into account.     

Parametric rolling prediction in irregular seas using combination of deterministic ship dynamics and probabilistic wave theory

In recent years there have been reports of serious accidents of parametric rolling for modern container ships and car carriers. For avoiding such accidents, a prediction method of parametric rolling in irregular seas is required. Since parametric rolling is practically non-ergodic, repetitions of numerical simulations or experiments could be not feasible to ascertain the behaviour. Therefore, in this paper, a method combining a stochastic approach with a deterministic approach in order to estimate the probabilistic index without such simple repetitions is developed. The ship's response in regular seas is estimated by solving an averaged system of the original 1-DoF roll model, and random waves necessary for occurrence of parametric rolling is achieved by using Longuet-Higgins’s or Kimura’s wave group theory. As a result, a fast and robust computation method of the probabilistic index is established. Finally, it is concluded that the proposed method is considered to be one of the useful tools for discussing the new IMO Intact Stability Code.     

An investigation of different methods for the prevention of parametric rolling

The parametric rolling of modern containerships is emerging as a serious problem, to the extent that its effects warrant a study into its prevention. In light of this, two methods for reduction of parametric rolling are proposed and examined by physical model experiments. The first is a sponson attached to the side of a ship, the purpose being to decrease the rate of change of the rollrestoring moment. The second is an antirolling tank to increase roll damping. By conducting free-running model experiments for a 6600-TEU post-Panamax container ship with sponsons under typical parametric rolling conditions, it was found that the sponsons could decrease the magnitude of parametric rolling. The antirolling tank could prevent parametric rolling completely in certain conditions, even in severe head seas. Using the damping coefficients from experimentally derived data of a model ship with an antiroll tank, a numerical simulation was established. The numerical model was then compared with the free-running model experiments. The results indicated that the numerical model could qualitatively verify the experimental results. Finally, an attempt to optimise the size of an antirolling tank for preventing parametric rolling for the subject post-Panamax container ship in the North Pacific Ocean is presented.     

Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit

The chaos that appears in the ship roll equation in beam seas known as the escape equation has been intensively investigated because it is closely related to capsizing incidents. In particular, many applications of the Melnikov integral formula have been reported in the literature; however, in all the analytical works concerning the escape equation, the Melnikov integral is formulated utilizing a separatrix for the Hamiltonian part or a numerically obtained heteroclinic orbit for the non-Hamiltonian part of the original escape equation. To overcome such limitations, this article attempts to utilise an analytical expression for the non-Hamiltonian part. As a result, an analytical procedure is provided that makes use of a heteroclinic orbit of the non-Hamiltonian part within the framework of the Melnikov integral formula.     

Broaching prediction in the light of an enhanced mathematical model,with higher-order terms taken into account

 We have attempted to develop a more consistent mathematical model for capsizing associated with surf-riding in following and quartering waves by taking most of the second-order terms of the waves into account. The wave effects on the hull maneuvring coefficients were estimated, together with the hydrodynamic lift due to wave fluid velocity, and the change in added mass due to relative wave elevations. The wave effects on the hydrodynamic derivatives with respect to rudder angles were estimated by using the Mathematical Modelling Group (MMG) model. Then captive ship model experiments were conducted, and these showed reasonably good agreements between the experiments and the calculations for the wave effects on the hull and the rudder maneuvring forces. It was also found that the wave effects on restoring moments are much smaller than the Froude–Krylov prediction, and the minimum restoring arm appears on a wave downslope but not on a wave crest amidship. Thus, an experimental formula of the lift force due to the heel angle of the ship is provided for numerical modelling. Numerical simulations were then carried out with these second-order terms of waves, and the results were compared with the results of free-running model experiments. An improved prediction accuracy for ship motions in following and quartering seas was demonstrated. Although the boundaries of the ship motion modes were also obtained with both the original model and the present one, the second-order terms for waves are not so crucial for predicting the capsizing boundaries themselves. Received: June 20, 2002 / Accepted: October 10, 2002 Acknowledgments. This research was supported by a Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 13555270). The authors thank Prof. N. Rakhmanin of the Krylov Ship Research Institute for providing the Russian literature, as well as Mr. H. Murata of NHK (Japan Broadcasting Corporation) for translating it into Japanese. Address correspondence to: N. Umeda (e-mail: umeda@naoe.eng.osaka-u.ac.jp)     

Effect of freeboard and metacentric height on capsizing probability of purse seiners in irregular beam seas

The probability of capsize of purse seiners in irregular beam seas and the effect of freeboard height and metacentric height on trapped water on the deck was investigated. The aim was to quantify a safety level that can be achieved by direct stability assessment for this type of fishing vessel. The amount of trapped water on deck was numerically estimated using a hydraulic flow assumption. The long-term capsizing probabilities were estimated using a piecewise linear approach together with wave statistics from major Japanese fishing areas. The estimated safety level of capsizing probability was compared with that obtained by the IMO weather criterion and by the water-on-deck criterion of the IMO Torremolinos Convention. Numerical results for four typical Japanese purse seiners indicated that the effect of freeboard, on the amount of trapped water on deck, is more important than that of the metacentric height. Besides the metacentric height and the freeboard, it was shown that the danger of capsizing is a function of the rise of floor. The safety level obtained by the capsizing probability approach is generally higher than that based on the IMO weather criterion. However, the water-on-deck criterion provides a higher safety level than the capsizing probability approach for ships with a low rise of floor.     

Broaching probability for a ship in irregular stern-quartering waves: theoretical prediction and experimental validation

To avoid stability failure due to the broaching associated with surf riding, the International Maritime Organization (IMO) has begun to develop multilayered intact stability criteria. A theoretical model using deterministic ship dynamics and stochastic wave theory is a candidate for the highest layer of this scheme. To complete the project, experimental validation of the theoretical method for estimating broaching probability in irregular waves is indispensable. We therefore conducted free-running model experiments using a typical twin-propeller and twin-rudder ship in irregular waves. A simulation model of coupled surge–sway–yaw–roll motion was simultaneously refined. The broaching probability calculated by the theoretical method was within the 95 % confidence interval of that obtained from the experimental data. This could be an example of experimental validation of the theoretical method for estimating the broaching probability when a ship meets a wave.