REPRESENTATION OF THREE-DIMENSIONAL PLANING SURFACES BY FINITE ELEMENTS

This paper presents a numerical solution for the the planing of a boat over the surface of deep water. The method applies to the case of a finite Froude number and an arbitrary beam, so that the restrictions of previous theories are avoided. Inviscid linearized potential flow is used. Thus the presence of the boat is modelled by the equivalent pressure distribution. The pressure itself is represented by a two-dimensional array of elements. The pressure is allowed to vary linearly with respect to position within each element so that the overall distribution is continuous. The wave pattern produced by one such element constitutes the first part of the solution. The second part of the solution is the assembly of these elements. Furthermore, the Kutta condition is satisfied at a discrete number of points along the trailing edge, and the boat must be in equilibrium. These extra conditions determine the rise and trim of the boat, as well as the extent of the wetted surface. With a very small number of elements in the longitudinal and transverse directions, the theory predicts the amount of wetted area of flat plates and prismatic hulls to within a few percent of that derived from experimental data. The proportion of the boat that rises out of the water is also computed to a similar accuracy. The lift coefficient tends to be about 30% low for a beam Froude number of two, but it is in better agreement at lower speeds.

  • Corporate Authors:

    University of New South Wales

    School of Mechanical and Industrial Engineering
    Kensington, New South Wales  Australia  2033
  • Authors:
    • Doctors, L J
  • Publication Date: 1975-9

Media Info

  • Features: References;
  • Pagination: 20 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00128642
  • Record Type: Publication
  • Source Agency: University of New South Wales
  • Report/Paper Numbers: NAV/ARCH/75/7
  • Files: TRIS
  • Created Date: Jan 14 1976 12:00AM