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