A Stability Analysis for Tethered Aerodynamically Shaped Balloons

Abstract

This work investigates the dynamic stability of tethered, aerodynamically shaped balloons by considering the system to pose essentially a cable problem, with the balloon's dynamics giving end and auxiliary conditions. This physical model gives a first-order problem in a sequence of partial differential wave equations with nonhomogeneous boundary conditions. Further, these 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, from which these roots are extracted by using an electronic computer and a roots locus plot. Further, this theory was applied toward the development of a highperformance tethered balloon design, and the results showed that good stability was attainable by the use of large and aerodynamically efficient fins.