Forces, moments, and added masses for Rankine bodies

Abstract

The dynamical theory of the motion of a body through an inviscid and incompressible fluid has yielded three relations: a first, due to Kirchhoff, which expresses the force and moment acting on the body in terms of added masses; a second, initiated by Taylor, which expresses added masses in terms of singularities within the bòdy; and a third, initiated by Lagally, which expresses the forces and moments in terms of these singularities. The present investigation is concerned with generalizations of the Taylor and Lagally theorems to include unsteady flow and arbitrary translational and rotational motion of the body, to present new and simple derivations of these theorems, and to compare the Kirchhoff and Lagally methods for obtaining forces and moments. In contrast with previous generalizations, the Taylor theorem is derived when other boundaries are present; for the added-mass coefficients due to rotation alone, for which no relations were known, it is shown that these relations do not exist in general, although approximate ones are found for elongated bodies. The derivation of the Lagally theorem leads to new terms, compact expressions for the force and moment, and the complete expressions of the forces and moments in terms of singularities for elongated bodies.

A numerical method for the evaluation of hydrodynamic forces of translating bodies under a free surface

“…Taylor's formula is then deemed necessary to evaluate added masses [25,32]. The second approch concerns the Lagally theorem, which expresses the dynamic effects in terms of singularities and gradients of velocity potential [33,34]. Although all results can presumably be obtained equally well by these three methods for the current problem, the proposed method appears to be more straightforward in mathematical formulation and easier in numerical implementation.…”

A numerical simulation of hydrodynamic forces of ground-effect problem using Lagrange's equation of motion

“…The unsteady Lagally theory [31,32] yields the expression of the ith force component acting on the moving body at a constant speed in the following:…”

Tensor Properties of Added-mass and Damping Coefficients

“…To study the behaviour of added-mass and damping tensors of a floating body under improper orthogonal transformations, we refer to Equation (6). In this equation, F i , U i , anḋ U i are components of three polar vectors and M i , i , and˙ i are components of three axial vectors.…”