Accession Number : AD0881790

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

Descriptive Note : Technical note,

Corporate Author : VON KARMAN INST FOR FLUID DYNAMICS RHODE-SAINT-GENESE (BELGIUM)

Personal Author(s) : DeLaurier, James D.

Report Date : DEC 1970

Pagination or Media Count : 124

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.

Descriptors :   , (*TOWED BODIES, STABILITY), (*TOWING CABLES, MATHEMATICAL MODELS), PHYSICAL PROPERTIES, STRESSES, MOORING, MATHEMATICAL PREDICTION, THEORY, BALLOONS, TOWED SONAR, FLUID DYNAMICS, MODEL THEORY, COMPUTER PROGRAMS, EQUATIONS OF MOTION, BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS, ACCELERATION, VELOCITY, PERTURBATION THEORY, MOMENTS.

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE