On the Floating Stability of Barges with Trapezoidal and Pentagonal Cross Sections

Stability problems concerning the symmetrical equilibrium position for barges floating in a liquid, which have trapezoidal and pentagonal cross sections, are discussed. The basic principles of static analysis required for studying the stability of floating bodies are given. For both problems the exact expression for the potential energy of a floating body is generated and its quadratic approximation is calculated near the investigated equilibrium state. With the help of these expressions the stability conditions are obtained in terms of dimensionless parameters and each of the problems is characterized by such three parameters. It is verified that for particular variants of a rectangular pontoon and a triangular boat, the previously known results follow from the found stability conditions in both problems. The found solutions are illustrated as a set of stability regions on the plane of two dimensionless parameters when the value of the third parameter is varied. This graphical interpretation makes it possible to find the main qualitative and quantitative features of the generated solutions and to make key conclusions. The obtained results are interesting from a theoretical point of view and may be used in practice.