A First Order Theory for Predicting the Stability of Cable Towed and Tethered Bodies Where the Cable has a General Curvature and Tension Variation.

Abstract

The cable-body system is treated analytically by considering it to be essentially a cable problem, where the body provides end and auxiliary conditions. Moreover, the cable itself is considered to be composed of cable segments - each with its own mean tension and angle. These segments are then matched - one to the next - by the end conditions of displacement and slope, thus yielding a physical model for a cable with a general shape and tension variation. The mathematical description of the first order form of this problem is a sequence of nonhomogeneous boundary value problems in linear partial differential wave equations, with linear ordinary differential end and auxiliary conditions. Further, the equations uncouple to give a 'lateral' problem and a 'longitudinal' problem - as in first order airplane dynamics. The solution of either problem takes the form of a transcendental characteristic equation for the stability roots. These roots are extracted by using an electronic computer and a roots locus plot. In order to provide a check on the theoretical analysis, a series of tests were performed on a cable-body system tethered in the V.K.I. open throat, low speed wind tunnel.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1970
Accession Number
AD0881790

Entities

People

  • James D. Delaurier

Organizations

  • von Kármán Institute for Fluid Dynamics

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Aircrafts
  • Airplanes
  • Boundaries
  • Boundary Value Problems
  • Computers
  • Curvature
  • Differential Equations
  • Displacement
  • Dynamics
  • Equations
  • Geometry
  • Mathematics
  • Sequences
  • Shape
  • Wave Equations
  • Wind Tunnels

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Marine Hydrodynamics
  • Structural Dynamics.

Technology Areas

  • Microelectronics