Contemporary Ideas on Ship Stability pp 51-76 | Cite as

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

## Abstract

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.

## Notes

### Acknowledgements

As stated in the Introduction, this work is a summary of *some* of the significant work contained in Sclavounos (2012), Sclavounos & Lee (2012) and Sclavounos, et al. (2019). The significant contribution of Paul Sclavounos is very much appreciated. The many fruitful discussions with the Theory Advisory Panel (TAP) are also appreciated; as are the efforts of Prof. Robert F. Beck of the University of Michigan and his graduate students Xinshu Zhang, Jim Bretl, Piotr Bandyk and Rahul Subramanian who provided the computational results reported herein. This work was supported by Drs. L. Patrick Purtell and Paul Hess of the Office of Naval Research (ONR).

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