An analytical study of fluid tank system for reducing the rolling of a ship

Abstract

There have long been attempts to reduce the rolling of ships, prompted by a desire to increase comfort of travel, improve weapon control measures, extend the operation of aircraft, and so on. In many passenger and naval ships anti-rolling tanks are fitted in order to reduce rolling. Anti-rolling tank systems operate on the principle that a fluid, usually water, moves from one tank to another and generates a moment on the ship that counteracts the rolling motion. The principal aim of the present paper is to explain the characteristics of oscillation of fluid in anti-rolling tanks. Using the principle of conservation of energy, a detailed theoretical analysis is performed for the oscillation of water in two identical circular tanks connected by a narrow pipe. A new expression is derived for the frequency of oscillation of water as a function of the diameter of the circular tanks, the depth of water in the tanks, and the length and diameter of the connecting pipe. Subsequently, the expression for the frequency of oscillation of water is modified for the case of two identical rectangular tanks. Then it is analytically demonstrated how the aforesaid tank system can be used to neutralize the rolling motion of a ship. Based on the aforesaid theoretical analysis, a computer program is developed in FORTRAN 95 and executed on the DELL OPTIPLEX 780 computer. The computational results are plotted in order to show how the frequency of oscillation of water is influenced by the diameter of the tanks, the depth of water in the tanks, geometry of the tanks and the length-to-diameter ratio of the connecting pipe. The present theoretical analysis is expected to be useful in the design of anti-rolling tanks which will effectively reduce the rolling motions of a ship.