Numerical simulation of longitudinal tackle oscillations when salvaging sunken vessels from deep water

A mathematical model is proposed for longitudinal oscillations of a tackle used for salvaging sunken vessels to the sea surface. The numerical approximation of the obtained model along the tackle rope length is accomplished by means of the finite-difference method. To implement this method, the transformation of independent coordinates is introduced into the constant step mesh. The integration with respect to time is carried out by the Φ-Wilson method. To solve the nonlinear systems of algebraic equations, iteration methods are used. There are examples of calculations for the vessel separation from the seabed and salvage from 1655 m depth when using various methods of controlling the winch shaft moment. The area of winch moment and heaving motion amplitude values that provide vessel emergency-free separation from seabed are calculated. It is shown that, with accuracy sufficient for practical use, the rope system of the tackle can be replaced in some cases by a single equivalent rope. Moreover, the rope mass can be neglected if it is considerably less than the mass of the vessel being salvaged. It is emphasized that the selection of the control of the velocity of salvage depends to a large extent on winch operation peculiarities.