Asymmetric water entry of a wedge

A mapping method of the complex analysis is used to study the water entry of asymmetric wedges. The problem is solved by using the expressions of the complex potential and velocity constructed by Chaplygin's singular points method extended to solve free boundary problems with an arbitrary boundary condition on the free surface. In this way the boundary value problem is reduced to a system of nonlinear equations including an integral and an integro-differential equation determining the angle and the modulus of the velocity along the free surface. The theoretical model is preliminary validated in the case of symmetric wedges through comparisons established with results provided by other theories available in literature. Hence the proposed model is applied to the case of asymmetric wedges and results are presented in terms of free surface shape, pressure distribution along the wedge sides and drag and moment coefficient. A parametric dependence on the main geometrical parameters is also evaluated.