Skip to main content
×
Home

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

  • T. Yao-Tsu Wu (a1) and Arthur K. Whitney (a1) (a2)
Abstract

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.

Copyright
References
Hide All
Cumberbatch, E.1958 Two-dimensional planing at high Froude number. J. Fluid Mech. 4, 466.
Miskhelishvili, N. I.1953 Singular Integral Equations. Groningen, Holland: Noordhoff.
Rispin, P. P. A.1967 A singular perturbation method for nonlinear water waves past an obstacle. Ph.D. thesis, California Institute of Technology.
Tricomi, F. G.1957 Integral Equations. Interscience.
Wehausen, J. V. & Laitone, E. V.1960 Surface Waves. Handbuch der Physik, vol. 9. Springer.
Whitney, A. K.1969 Minimum drag profiles in infinite cavity flows. Ph.D. thesis, California Institute of Technology.
Wu, T. Y.1967 A singular perturbation theory for nonlinear free-surface flow problems. International Shipbuilding Progress, 14, 88.
Wu, T. Y. & Whitney, A. K.1971 Theory of optimum shapes in free-surface flows. Part 1. California Institute of Technology Rep. E 132 F. 1.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 69 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th November 2017. This data will be updated every 24 hours.