A FLAT CYLINDER THEORY FOR VESSEL IMPACT AND STEADY PLANING RESISTANCE

This work has been motivated by the need for an alternative hydrodynam ic theory to apply in analysis of impact loads on typical sections of vessels operating in waves, as well as for the closely analogous hydro dynamics of steady planing in calm water. A theory is needed which is computationally practical, but also physically sound, and incorporatin g the needed level of sensitivity to detail in the driving physical va riables. A new theory believed to achieve this objective is proposed h erewith. It can be viewed as a rational compromise between direct nume rical inversion of the relatively exact governing equations, which is not presently possible to the needed level of generality, and the simp le asymptotic theories evolved from the original work of Herbert Wagne r (1932). The single solution field of the exact formulation is retain ed 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 reta ins the hydrodynamic nonlinearity of the exact formulation; the transv erse flow perturbation is retained in the axis boundary conditions to consistent order. As contour flatness is approached and geometric line arity is more and more closely achieved, the transverse contour veloci ty becomes increasingly larger. The achievement of uniform geometric l inearity in the flatness limit is therefore accompanied by uniform hyd rodynamic nonlinearity. This is not recognized in the asymptotic theor ies, where the far field is linear both geometrically and hydrodynamic ally. The reduction of the exact formulation to an axis satisfaction o f the boundary conditions allows much of the geometric inversion imbed ded within the initial value problem to be performed analytically. Thu s the outer numerical time integration of the system is in terms of st able algebraic formula, resulting in algorithms that are reliably comp utable on standard computing equipment. Discretization of the general theory for numerical analysis is proposed. The analysis procedure deve loped is applied to a number of cases of generalized flat cylinder imp act. This is in the interest of demonstrating both its utility and its value in providing new insight into the very complex character of imp act hydrodynamics.