Journal of Engineering Mathematics

, Volume 58, Issue 1–4, pp 91–107 | Cite as

The influence of gravity on the performance of planing vessels in calm water

  • Hui Sun
  • Odd M. Faltinsen
Original Paper


Usually gravity can be neglected for planing vessels at very high planing speed. However, if the planing speed becomes lower, the influence of gravity must be considered. A 2D+t theory with gravity effects is applied to study the steady performance of planing vessels at moderate planing speeds. In the framework of potential theory, a computer program based on a boundary-element method (BEM) in two dimensions is first developed, in which a new numerical model for the jet flow is introduced. The spray evolving from the free surface is cut to avoid the plunging breaker to impact on the underlying water. Further, flow separation along a chine line can be simulated. The BEM program is verified by comparing with similarity solutions and validated by comparing with drop tests of V-shaped cylinders. Then the steady motion of prismatic planing vessels is studied by using the 2D+t theory. The numerical results are compared with the results by Savitsky’s empirical formula and the experiments by Troesch. Significant nonlinearities in the restoring force coefficients can be seen from the results. Three-dimensional effects are discussed to explain the difference between the numerical results and the experimental results. Finally, in the comparison of results at high planing speed and moderate planing speed, it is shown that the gravity not only affects the free-surface profile around the hull, but also influences the hydrodynamic force on the hull surface.


Boundary-element method Gravity effect Planing vessel Three-dimensional effect 2D+t theory 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Centre for Ships and Ocean StructuresNorwegian University of Science and TechnologyTrondheimNorway

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