Hydrodynamic coefficients of an elongated body rapidly approaching a free surface

A hydrodynamic analysis is made for the motion of a submerged, elongated body of revolution rapidly approaching a free-surface with longitudinal, transverse, and rotational velocities, and an arbitrary angle of attack. Axial doublet distributions are used to generate the flowfield and the prescribed body shape. The hydrodynamic forces and moments acting on the body are determined by the generalized Lagally theorem. Expressions for the hydrodynamic force and moment are derived and numerical solutions for the hydrodynamic coefficients are obtained. Through the characteristics behavior of these coefficients, effects of the free surface on the body dynamics are examined.