The configuration of a cable towed in a circular path

The problem of determining the equilibrium configuration of a cable towed in a circular path has both mathematical and practical interest. Mathematically, this interest is generated because of the multivalued nature of the boundary value problem. Practically, this interest arises because the towed drogue, for certain ranges of the governing parameters, obtains an equilibrium position very near the axis of rotation thus enabling pinpoint deliveries of payloads from fixed-wing aircraft. In this paper, the circular towing problem for a flexible, inextensible cable is examined. The equations of equilibrium and the boundary conditions which govern the cable configuration are derived and nondimensionalized to isolate the important parameters. The significance of these parameters for modeling the towing system is discussed. Finally, extensive numerical results are obtained for a particular airborne system. This example shows that an intimate relation exists between the mathematically interesting multivalued regions of solution and the practically interesting regions for which large towline verticality and small drogue radius are simultaneously present.