Equilibrium configurations of flying cables of captive balloons, and cable derivatives for stability calculations

Abstract

The theory of equilibrium of balloon flying cables is presented in a simplified form most suitable for applications, with numerical tables covering probably the full range of practical cases. A simplified derivation of formulae for longitudinal cable derivatives is presented, and the problem of the lateral cable derivative solved. The normal oscillatory modes of the 'balloon-plus-cable' system (longitudinal and lateral, ignoring balloon aerodynamics) are determined and analysed. All final formulae are expanded into power series which converge well in the important case of a highly tensioned cable. The report provides the data necessary for studying dynamic stability of captive balloons.