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Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface

Wu, T. Yao-tsu and Whitney, Arthur K. (1972) Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface. Journal of Fluid Mechanics, 55 (3). pp. 439-455. ISSN 0022-1120. doi:10.1017/S0022112072001946.

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This paper attempts to determine the optimum profile of a two-dimensional plate that produces the maximum hydrodynamic lift while planing on a water surface, under the condition of no spray formation and no gravitational effect, the latter assumption serving as a good approximation for operations at large Froude numbers. The lift of the sprayless planing surface is maximized under the isoperimetric constraints of fixed chord length and fixed wetted arc-length of the plate. Consideration of the extremization yields, as the Euler equation, a pair of coupled nonlinear singular integral equations of the Cauchy type. These equations are subsequently linearized to facilitate further analysis. The analytical solution of the linearized problem has a branch-type singularity, in both pressure and flow angle, at the two ends of plate. In a special limit, this singularity changes its type, emerging into a logarithmic one, which is the weakest type possible. Guided by this analytic solution of the linearized problem, approximate solutions have been calculated for the nonlinear problem using the Rayleigh-Ritz method and the numerical results compared with the linearized theory.

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Additional Information:© 1972 Cambridge University Press. Received 8 September 1971 and in revised form 6 July 1972. Published online: 29 March 2006. This work was carried out under the support of the Naval Ship System Command General Hydrodynamics Research Program, administered by the Naval Ship Research and Development Center and the Office of Naval Research, under contract 220 (51).
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Naval Ship Research and Development Centre (NSRDC)UNSPECIFIED
Office of Naval Research (ONR)220 (51)
Issue or Number:3
Record Number:CaltechAUTHORS:20120806-160202833
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32958
Deposited By: Tony Diaz
Deposited On:06 Aug 2012 23:15
Last Modified:09 Nov 2021 21:31

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