Marine Technology - April 2008 - Page#65

<BODY> <span id="lblContents">down flooding, cargo shift or loss, and a number of other dangerous and undesirable consequences. As the development of large roll angles involves the same physical mechanism as capsizing, it makes sense to include these events as another type of stability failure. A similar failure event may have large roll accelerations that are closely correlated with roll motions in irregular seas. A partial stability failure is defined as an event that includes the occurrence of very large roll angles and/or excessive roll accelerations that will not result in loss of the ship, but that could impair normal operation of the ship and could be dangerous to crew, passengers, cargo, or ship equipment. The above definition covers cases of parametric roll as well as cases of broaching and pure loss of stability that only resulted in large roll angle but did not lead to capsizing. 2.4. Modes of stability failures Based on the extended discussion, the 48th session of the SLF SubCommittee of the IMO defined three distinct physical phenomena responsible for stability failures: ? Variation of the restoring moment in waves ? Instability in the dead-ship condition ? Maneuvering-related failures. Physical mechanisms of these phenomena are meant to be modeled within performance-based criteria. A rather complete overview of capsize modes is provided in ITTC (1999). 2.4.1. Variation of restoring moment in waves. The first mode of stability failure is related to righting-arm variations in waves; the restoring moment becomes larger in the wave trough and smaller on the wave crest. This is mainly the result of the changing submerged hull geometry. This effect has been known to naval architects for a long time (for example, Paulling 1961). Figure 1 illustrates these changes. Most vessels have relatively slender lines at the fore and aft ends to decrease wave resistance and facilitate proper flow into the propeller. Further up, the lines become wider; bow flare is needed to protect the deck from the green water in rough weather, while stern overhang is fitted to protect the propeller and provide a place for a steering gear. When a vessel is designed to carry relatively light cargo (such as containers), volumetric capacity becomes a design requirement and this tendency becomes especially pronounced. The effect of wave on ship stability is most evident when a ship is sailing in following or head seas and when the wave length is comparable to the ship length. When a wave trough is amidships, relatively wide sections fore and aft are submerged and the actual waterline becomes wider compared with calm water. The instantaneous value of BM is related to instantaneous waterline width BMW = 2 3 W 0.5L -0.5L yW x 3 dx (1) Here, BMW is the BM calculated for the actual wave waterline; yW(x) are half-breadths at actual water level at each station, located at distance x from midship section; W is volumetric displacement calculated up to the actual waterline; and L is ship length. As can be clearly seen from equation (1), a wider waveinduced waterline produces a larger BM, which leads to an increase of characteristics of initial stability. On the other hand, when a wave crest is near amidships, the waterline intersects the slender parts of the hull lines (see Fig. 1). The wave-induced waterline becomes more narrow, which leads to a decrease in initial stability according to equation (1). These changes in stability go beyond initial stability. The GZ curve also changes as the wave passes (see Fig. 2 where the GZ curves for the wave crest and trough are shown for a post-Panamax containership). However, physical reasons of stability changes in waves are not limited to forces of hydrostatic nature. Pressure in waves is distributed differently than in calm water, so the Smith effect also contributes, as well as steady ship waves and radiated and diffracted waves. Nevertheless, hydrostatic calculations remain a common way to evaluate stability in following and head seas. ABS (2004) recommends using hydrostatic calculations for initial analysis of susceptibility of containership to parametric roll. Hydrostatic tools were also used by Womack and Johnson (2005) for analysis of stability of fishing vessels in waves (this paper also contains a comprehensive review of capsizing experiments). Changing stability in waves invokes two physical modes of stability failure: pure loss of stability and parametric roll resonance. Pure loss of stability in waves occurs when a vessel encounters a single large wave in following or quartering seas and spends a considerable amount of time on the wave crest. If stability of the vessel on the wave crest deteriorates too much, the vessel may capsize or attain a very large heel angle. To illustrate a stability failure, consider a single-degree-offreedom, nonlinear differential equation of roll: IX + A44 ? + FRD , + GZ , t = H t (2) Here, the symbol stands for roll angle (a dot above this symbol signifies derivative with respect to time; a single dot means roll rate, while two dots means roll acceleration); IX is the mass moment of inertia; A44 is the added moment of inertia; FRD is a term expressing roll damping; is the displacement of the vessel expressed in terms of weight; GZ is the righting arm, taking into account stability change in Fig. 1 Stability change in waves (dashed line corresponds to a waterline in calm water) Fig. 2 Changes of the GZ curve in waves APRIL 2008 MARINE TECHNOLOGY 103</span> <br /> <br /> <a href="http://www.digitalwavepublishing.com/" title="Digital Magazine">Digital Wave Publishing</a> </BODY>