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

  • Arthur M. ReedEmail author
  • John G. Telste
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 119)


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.



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).


  1. Bandyk, P. J. (2009) A Body-Exact Strip Theory Approach to Ship Motion Computations. Ph.D. Dissertation, Univ. Mich., Ann Arbor, MI, xii+122 p.Google Scholar
  2. Belknap W. and J. Telste (2008) Identification o fLeading Order Nonlinearities from Numerical Forced Motion Experiment Results. Proc. 27thSymp. NavalHydro., Seoul, Korea, 18 p.Google Scholar
  3. Lighthill, M.J. (1960) A Note on the Swimming of Slender Fish.J. Fluid Mech., 9:305–317.MathSciNetCrossRefGoogle Scholar
  4. Newman, J.N. (1977) MarineHydrodynamics. MIT Press, xiii + 402 p., Cambridge, MA.Google Scholar
  5. Newman, J. N. & T. Y. Wu (1973) A Generalized Slender-Body Theory for Fish-Like Forms. J. Fluid Mech., 57(4):673–693.CrossRefGoogle Scholar
  6. O’Dea, J. F., E. J. Powers and J. Zselecsky (1992) Experimental Determination of Nonlinearities in Vertical Plane Ship Motions. Proc. 19th Symp. Naval Hydro., Seoul, Korea, pp. 73–91.Google Scholar
  7. Ogilvie, T. F. and E. O. Tuck (1969) A rational strip theory of ship motions: Part I. Dept. of Nav. Arch. and Marine Eng., College of Eng., Univ. Michigan, Report No. 013, ix+92 p.Google Scholar
  8. Reed, A.M. and J.G.Telste (2011) Computing Hydrodynamic Forces and Moments on a Vessel without Bernoulli’s Equation. Proc. 12th Int’l Ship Stability Workshop, Washington, D.C., pp. 341–51.Google Scholar
  9. Reed, A.M. (2012) Application of Computing Hydrodynamic Forces and Moments on a Vessel without Bernoulli’s Equation.Proc. 11th International Conference on the Stability of Ships and Ocean Vehicles, Athens, Greece pp. 853–63.Google Scholar
  10. Salvesen, N., E. O. Tuck & O. Faltinsen (1970) Ship motions and sea loads. Trans. SNAME, 78:250–87.Google Scholar
  11. Sclavounos, P. D. (2012) Nonlinear Impulse of Ocean Waves on Floating Bodies. J. Fluid Mech., 697:316–35.MathSciNetCrossRefGoogle Scholar
  12. Sclavounos, P. D. and S. Lee (2012) A Fluid Impulse Nonlinear Theory of Ship Motions and Sea Loads. Proc. 29th Symp. Naval Hydro., Gothenburg, Sweden, 14 p.Google Scholar
  13. Sclavounos, P.D., J.G.Telste and A.M.Reed (2019) Modeling of Nonlinear Vessel Responses in Steep Random Waves. Carderock Division, Naval Surface Warfare Center Report (to be published).Google Scholar
  14. Serrin, J. (1959) Mathematical principles of classical fluid mechanics. Encyclopedia of Physics, Vol. VIII/Fluid Dynamics I, pp. 125–263, Springer-Verlag, Berlin.Google Scholar
  15. Smirnov, V. I. (1964) A Course of Higher Mathematics, Vol. II: Advanced Calculus. Pergamon Press, 630 p., Oxford.Google Scholar
  16. Telste, J.G. and W.F. Belknap (2008) Potential Flow Forces and Moments from Selected Ship Flow Codes in a Set of Numerical Experiments. Carderock Division, Naval Surface Warfare Center Report NSWCCD-50-TR-2008/040,15,240p.Google Scholar
  17. Vugts, J. H. (1968) The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface, Int’l Shipbuilding Prog., 15(167):251–76.CrossRefGoogle Scholar
  18. Watanabe, I., M. Ueno, H. Sawada (1989) Effects of Bow Flare Shape to the Wave Loads of a container ship. J. Society Naval Architects of Japan, 166:259–66.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.David Taylor Model Basin (NSWCCD)West BethesdaUSA

Personalised recommendations