A first order theory for predicting the stability of cable towed and tethered bodies where the cable has a general curvature and tension variation

The objective of this research was to investigate the dynamics of cable-body systems, and ~n particular, to develop an analysis for finding the stability of towed and tethered bodies in a fluid stream. Particular applications for which the analysis may be used include towed underwater devices, towed and tethered finned balloons, towed reentry decelerators, and towed airborne devices. 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 non homogeneous 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 we re performed on a cable-body system tethered in the V.K.I. open throat, low speed wind tunnel. The quantities measured were the system's longitudinal and lateral frequencies of oscillation and stability boundaries. Since this test system contained most of the essential features of the theory, and since the theoretical results and experimental results compared favorably, it is felt that this analysis provides a reasonable method for treating the first order motion of a large variety cable-body systems.