Variational principle for determining the unknown wetted surface of a planing ship |
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Authors: | Kiyoshige Matsumura Tokihiro Katsui |
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Institution: | (1) Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan, JP;(2) NKK Corportation, Kumozu, Kokan-cho, Tsu, Mie 514-0301, Japan, JP |
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Abstract: | A variational principle is presented to solve the problem of determining the unknown wetted surface of a planing ship on
still water under gravity. The functional associated with the variational principle is expressed by the unknown wetted length
distribution, the vortex line function, and the circulation distribution around the longitudinal sections, not by the bottom
pressure distribution. In addition, the variational principle is adjoined with pseudoflow, here called reverse flow. The extremal
of the functional satisfy the hull boundary integral equation in a similar way to that of lifting-surface theory and the elevated
water surface condition along the spray root line. Both are sufficient to determine the wetted surface. A method of high aspect
ratio approximation is also investigated. A simple relation is obtained between the wetted surface when moving and at standstill.
The calculated shapes of the wetted surface of a planing plate agreed well with experimental results.
Received for publication on Nov. 11, 1999; accepted on April 4, 2000 |
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Keywords: | : variational principle unknown boundary problem planing ship |
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