4. Application of Computing Hydrodynamic Forces and Moments on a Vessel Without Bernoulli’s Equation

Traditionally the hydrodynamic force on a ship’s hull is obtained by integrating the pressure over the hull, using Bernoulli’s equation to compute the pressures. Due the need to evaluate \(\varPhi _t\), \(\varPhi _x\), \(\varPhi _y\), \(\varPhi _z\) at every instant in time, this becomes a computational challenge when one wishes to know the hydrodynamic forces (and moments) on the instantaneous wetted surface of a vessel in extreme seas. A methodology that converts the integration of the pressure over the hull surface into an impulse, the time derivative of several integrals of the velocity potential over the surface of the vessel and possibly the free surface near the vessel is introduced. Some examples of applying the impulsive theory to 2- and 3-dimensional bodies are presented.