Three-Dimensional Planing at High Froude Number

Abstract

The steady motion of a planing surface of moderate aspect ratio at small angles of attack is considered. Linearized theory is used with a square- root type of pressure singularity representing the flow near the leading edge. As asymptotic solution for the pressure distribution on the planing surface at large Froude number (or small beta, the inverse of the Froude number) is sought. The lowest order term of the pressure distribution, obtained by setting beta equal to zero, is found to be the same as the pressure distribution on the lower side of the corresponding thin wing. Higher order terms in beta are obtained by an iteration process. Explicit solutions are obtained to order beta squared for rectangular planforms. Numerical results are calculated for rectangular flat plate planing surfaces of aspect ratios from 0.5 to 2.0. It is found that for large aspect ratios the lift coefficient is reduced by the gravity effect and for small aspect ratios it is increased, the dividing aspect ratio being about 1.5. The results compare reasonably well with experimental data.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 19, 1970
Accession Number
AD0717067

Entities

People

  • D. P. Wang
  • Paul Rispin

Organizations

  • The Catholic University of America

Tags

Communities of Interest

  • Air Platforms
  • Ground and Sea Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Aspect Ratio
  • Bessel Functions
  • Boundaries
  • Equations
  • Flow
  • Froude Number
  • Integral Equations
  • Leading Edges
  • Planform
  • Planing Surfaces
  • Pressure Distribution
  • Square Roots
  • Thin Wings
  • Three Dimensional
  • Trailing Edges
  • Two Dimensional
  • United States

Fields of Study

  • Physics

Readers

  • Aerodynamics/Aeronautics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Marine Hydrodynamics