A Flat Cylinder Theory for Vessel Impact and Steady Planing Resistance

Abstract

This work has been motivated by the need for an alternative hydrodynamic theory to apply in analysis of impact loads on typical sections of vessels operating in waves, as well as for the closely analogous hydrodynamics of steady planing in calm water. A theory is needed which is computationally practical, but also physically sound, and incorporating the needed level of sensitivity to detail in the driving physical variables. A new theory believed to achieve this objective is proposed herewith. It can be viewed as a rational compromise between direct numerical inversion of the relatively exact governing equations, which is not presently possible to the needed level of generality, and the simple asymptotic theories evolved from the original work of Herbert Wagner (1932). The single solution field of the exact formulation is retained in the proposed theory; this is versus separate near and far fields of the asymptotic methods. The major reduction of the exact equations exercised here is the specification of uniform first-order geometric linearity; this is also an implicit characteristic of the Wagner class of asymptotic theories. All boundary conditions are satisfied on the horizontal axis in the limit of flatness. But the proposed theory retains the hydrodynamic nonlinearity of the exact formulation; the transverse flow perturbation is retained in the axis boundary conditions to consistent order. As contour flatness is approached and geometric linearity is more and more closely achieved, the transverse contour velocity becomes increasingly larger. The achievement of uniform geometric linearity in the flatness limit is therefore accompanied by uniform hydrodynamic nonlinearity. This is not recognized in the asymptotic theories, where the far field is linear both geometrically and hydrodynamically. The reduction of the exact formulation to an axis satisfaction of the boundary conditions allows much of the geometric inversion imbedded within the initial value problem to be performed analytically. Thus the outer numerical time integration of the system is in terms of stable algebraic formula, resulting in algorithms that are reliably computable on standard computing equipment. Discretization of the general theory for numerical analysis is proposed. The analysis procedure developed is applied to a number of cases of generalized flat cylinder impact. This is in the interest of demonstrating both its utility and its value in providing new insight into the very complex character of impact hydrodynamics.