Application of added mass theory in planing
Prediction of the hydrodynamic forces on planing craft by strip method requires the force acting on two-dimensional sections in vertical motion on the free surface to be known. The motion of a transverse section of a prismatic hull in steady planing corresponds to a constant velocity water entry of a wedge shaped section. The force acting on the wedge section before the chines get wetted is found from a consideration of the rate of change of the section added mass. The current added mass impact theory does not give a satisfying definition of the change in added mass after chines wetting, and hence predictions of non-constant velocity water entry can not be made accurately. As a consequence, the theory is not applicable for use in prediction of the lifting force on hulls in unsteady planing or on hulls in steady planing with non-straight keel line, i.e. phenomena corresponding to non-constant water entry. Also, in unsteady planing, sections experience exit motion due to the pitch and heave response of the craft. If applying the added mass theory in exit predictions, the resulting force acts in the direction of motion, something in contradiction with intuition and common sense. The work described in this thesis has resulted in a new added mass theory for water entry and exit of transverse sections of typical planing craft. A program of numerical simulations and experiments with wedge shaped sections has been carried out, providing force data for water entry and exit of such bodies to and from the water. Analysis of these data have led to separation of the added mass and damping forces and to the development of quasi-empirical expressions applicable for both constant and non-constant velocity force predictions. Thus the new theory provides a basis for strip method for prediction of the unsteady motion forces of planing craft. Further, the new added mass theory for water entry has been applied to predict the steady planing lift force on slender body hulls, and consistency with published planing data has been found. Also, an empirical aspect ratio correction has been derived, allowing application to large aspect ratio (non-slender) planing hulls.