IMO REVISION OF THE INTACT STABILITY CODE. Proposal of methodology of direct assessment for stability under dead ship condition. Submitted by Japan

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1 INTERNATIONAL MARITIME ORGANIZATION E IMO SUB-COMMITTEE ON STABILITY AND LOAD LINES AND ON FISHING VESSELS SAFETY 49th session Agenda item 5 SLF 49/5/5 19 May 2006 Original: ENGLISH REVISION OF THE INTACT STABILITY CODE Proposal of methodology of direct assessment for stability under dead ship condition Submitted by Japan Executive summary: Action to be taken: Paragraph 15 SUMMARY This document proposes a methodology of direct assessment for stability under dead ship condition. It is suggested that this proposal is discussed as a first step towards performance-based stability criteria to be included in the Intact Stability Code. Related documents: SLF 48/4/1, SLF 48/4/14, SLF 48/21 and SLF 49/5/1 INTRODUCTION 1 The Sub-Committee, at its forty-eighth session, agreed that performance-based criteria should be developed as part of the revision of the IS Code (resolution A.749(18), as amended), taking into account the dynamic phenomena in seaways. As shown in annex 3 of document SLF 48/4/1, these phenomena should include: a) restoring arm variation problems such as parametric excitation and pure loss of stability, b) stability under dead ship condition defined by SOLAS regulation II-1/3-8, and c) manoeuvring related problems such as broaching-to. In addition, numerical simulation and/or analytical methods validated with model experiments are expected to be utilized as a basis of probabilistic stability assessment. 2 Responding to this situation, Japan herewith proposes a methodology of the probabilistic assessment for stability under dead ship condition based on its own latest research. Here the dead ship condition is the condition under which the main propulsion plants, boilers and auxiliaries are not in operation due to the absence of power. In a case where the geometry of a ship is longitudinally symmetric and the wave direction coincides with the wind direction, the ship could suffer beam wind and waves. Thus, it is necessary, in general, to deal with ship behaviour in oblique wind and waves. For reasons of economy, this document is printed in a limited number. Delegates are kindly asked to bring their copies to meetings and not to request additional copies.

2 SLF 49/5/ Based on the above, the proposed methodology consists of the following three steps. Firstly, a drift motion including the drift velocity and the heading angle is numerically predicted. Secondly, an hourly-capsizing probability under the drifting motion in stationary random wind and waves is theoretically estimated. Thirdly, a capsizing probability per ship per year is calculated with wind and wave statistics. Then it is possible to compare the capsizing probability with the acceptable safety level. PREDICTION OF DRIFT MOTION 4 If a ship is situated in deterministic wind and waves without forward velocity, the ship may normally have a constant drifting velocity and heading angle, which can be regarded as a stable equilibrium, or a periodic motion around an unstable equilibrium. For predicting such drifting behaviour, it is necessary to identify fixed points of an equation set of surge-sway-yaw-roll motions and to examine local stability at the fixed point. 5 Even under the assumption of deterministic environment, the following items should be specified:.1 wind speed and wind direction,.2 wave height, period and direction,.3 hull geometry and mass distribution. 6 The ship motion can be assumed to consist of a surge-sway-yaw-roll slow motion with large magnitude and sway-heave-roll-pitch-yaw fast motion with small amplitude. Here the fast motion has a frequency comparable to the wave frequency. Thus, the fast motion is dealt with a linear potential theory, such as a slender body theory in waves. For the slow motion, steady wind forces and moments are estimated with empirical formulae, steady wave forces and moments are calculated with a combination of momentum and energy conservation laws and low-speed manoeuvring forces and moments due to large-scale flow separation were modelled with captive test data. 7 Since the obtained equation of the slow motion is non-linear, it can be solved by the Newton method with tracing solutions as a function of control parameter such as the angle between wind and waves. Because of non-linearity, more than one solution could exist. Thus, it is necessary to examine its local stability by calculating the eigenvalues of the system defined by the equation of the slow motion. If all real parts of the eigenvalues are negative, the equilibrium is stable and can be realized. If not, it is unstable. The output here is surge velocity, sway velocity, heading angle and heel angle. Table 1. Principal dimensions of the RoPax ferry Length between perpendiculars 170 m Area of bilge keel m 2 Breadth 25 m Vertical centre of gravity m Depth 14.8 m Designed metacentric height 1.41 m Draught 6.6 m Flooding angle 39.5 degrees Block coefficient Roll period m Lateral projected area: AL 3,433 m 2 Wind heeling lever 7.91 m Height of centre of AL above WL 9.71 m N coefficient at 20 degrees

3 - 3 - SLF 49/5/5 X Wind χ U x β 0' ψ 0 y W ave Y Figure 1. Co-ordinate systems and wind and wave directions sway velocity (m/ Stable U nstable angle between wind & waves (degrees) Figure 2. Sway velocity of the RoPax ferry under dead ship condition 8 The above method was applied to a 170 m long RoPax ferry, which was used for the model experiment described in the annex of document SLF 49/5/1. Its principal particulars are shown in Table 1. The co-ordinate system used here is defined in Figure 1 together with wind and wave directions. The surge and sway velocities are defined as the ship velocities in x and y axis, respectively. The heading angle is done with the symbol ψ and the heel angle is a rotation around the x axis. A numerical example is shown in Figures 2 and 3. Here the wind velocity, wave height and period are set to be equal to the weather criterion. Thus the wind velocity is 26 m/s, the wave period is equal to the ship natural roll period and the wave steepness is specified with the table in the weather criterion. The angle between wind and wave, χ, systematically varies from 0 degrees to 180 degrees. Here 0 degrees indicates the case where the wind direction coincides with the wave direction, which is assumed in the weather criterion. In this case, the ship suffers almost beam wind and waves and drifts toward leeward with the speed of 2 m/s. When the relative wave direction increases, two stable equilibria coexist: one is bow waves and the other is quartering waves. When the relative angle exceeds a threshold, one of them becomes unstable and a periodic motion around it emerges in bow wave condition. These results could depend on hull forms above and under water surface.

4 SLF 49/5/ The above discussion was limited to deterministic environment. Developing a method in random environment is a task for the future. It is also requested to validate the above method with model experiment although partial validations were reported heading angle (degree Stable Unstable angle between wind & waves (degrees) Figure 3. Heading angle of the RoPax ferry under dead ship condition PREDICTION OF CAPSIZING PROBABILITY IN STATIONARY ENVIRONMENT 10 Once the drifting velocity and attitude are determined, it is possible to calculate capsizing probability in irregular wind and waves. The method is based on Belenky s piece-wise linear method, and was already described by Japan in document SLF 48/4/14, but only for beam wind and waves. For taking drifting effects into account, the excitation frequency should be estimated as the encounter frequency and effective wave slope coefficient and the wind heeling lever are assumed to be proportional to sinusoidal functions of heading. Here the effective wave slope coefficient in beam waves, roll damping moment and the wind heeling lever in beam wind were estimated with the model tests following the interim guideline described in document SLF 48/21. The measured effective wave slope coefficient is 0.77 while the estimation with a strip theory is For this particular ship, theoretical prediction of effective wave slope coefficient seems to be acceptable. Further validation efforts are desirable. 11 The numerical example of hourly capsizing probability for the RoPax ferry is shown in Figure 4. The maximum capsizing probability here is about 10-20, and appears at the angle between wind and waves of 0. In this case the ship suffers almost beam wind and waves. This result demonstrates, within the assumption used here, that the ship can be regarded as safe against capsizing if capsizing probability in beam wind and waves is sufficiently low, although the ship under dead ship condition may have different drifting attitude depending on the angle between wind and waves. It is noteworthy that this analysis does not consider parametric roll, which should be separately discussed.

5 - 5 - SLF 49/5/ E E E E-09 capsizing probabi 1.00E E E E E E E E E-36 angle betw een w ind & w aves (degrees) Figure 4. Hourly capsizing probability for various angles between wind and waves hourly capsizing possibility E+00 RoPax ferry 1.00E-02 (L=170m) 1.00E-04 Acceptable level 1.00E-06 current design 1.00E E-10 current weather criterion 1.00E-12 experiment-supported weather 1.00E-14 criterion 1.00E E E-20 Assumed value of weather criterion wind velocity(m/s) Figure 5. Safety level estimated with hourly capsizing probability PREDICTION OF CAPSIZING PROBABILITY PER SHIP PER YEAR 12 By considering wave and wind statistics, we may average the hourly capsizing probabilities in various stationary sea states specified with mean wind velocity, significant wave height and mean wave period. Then the probability of capsizing per ship per year, P, can be calculated as follows: P = 1 (1 p) where p indicates the mean of averaged hourly capsizing probability. If the value of P is below the allowable level, the ship can be regarded as safe.

6 SLF 49/5/ If the safety of shipping is requested to be similar to other industrial activities, the allowable level may exist within a fuzzy band from 10-5 to And, if occurrence of the sea state represented with the mean wind velocity of 26 m/s is assumed to be about 10-4, the allowable hourly capsizing probability under the wind velocity of 26 m/s is from 10-5 to For comparing the safety level with this reference, the hourly capsizing probabilities are calculated for the designed metacentric height, the metacentric height marginally complying with the current weather criterion and that with the experiment-supported weather criterion agreed (SLF 48/21). The results shown in Figure 5 indicate that the current weather criterion requires sufficiently small capsizing probability and the experiment-supported weather criterion requests the capsizing probability that is almost similar to the allowable safety level in other industrial activities. CONCLUSIONS 14 Japan is of the opinion that the methodology presented here can be used as a basis for further discussion towards the establishment of performance-based criteria. Even if we limit ourselves to the beam sea assessment, the proposed methodology requires certain efforts so that it seems to be suitable for alternative means to prescriptive criteria for new ship types. It is also important to establish the safety level of the existing prescriptive criteria by utilizing this proposed methodology. ACTION REQUESTED OF THE SUB-COMMITTEE 15 The Sub-Committee is invited to consider the above proposal of methodology for directly assessing stability under dead ship condition and take action as appropriate.

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