Stability Index for Rectangular-Hulled Floating Bodies

Abstract

In this study, we propose the righting moment rate (Rr) as a new stability index for rectangular hulls; the hulls of such a shape have both a lower height and larger width than ships, and they are used for work vessels without a propulsion unit. In naval architecture and marine engineering, the metacentric height (GM) is one of the most basic stability indexes. The numerical range of GM has been historically shown for typical classes of ships at their corresponding times. However, the GM for work vessels with rectangular hulls is substantially larger than that for ships; this is problematic because work vessels can therefore incorrectly be deemed stable. Thus, we propose Rr as a new stability index for rectangular hulls to avoid faulty stability evaluations. In this study, we use examples of work vessels (e.g., crane barges) and ships (e.g., freight vessels) to clarify the differences between their respective stabilities. Hull depth, draft, center of gravity height, center of buoyancy height, and GM were modeled for rectangular hulls and ship-shaped hulls based on these examples. We determined the characteristics of the buoyancy, gravity, and righting moments, as well as the difference between the buoyancy moment and the gravity moment acting on each respective hull. In this manner, an adequate correlation between Rr and GM as stability indexes was both confirmed and determined theoretically.