Unwinding characteristics of thin cables for inner and outer dispensers

When thin cables of materials such as yarn and tether are unwound from a spool dispenser, various balloon shapes are generated depending on the initial tensile force at the guide-eyelet point. The shapes are dependent on the properties of the cable because the point of unwinding depends on the thickness of the cable. In this paper, the unwinding characteristics are analyzed for inner and outer dispensers by using three types of thin cable. The dimensionless steady-state equation of motion is first derived from Hamilton's principle for an open system and the perturbation scheme. The second-order differential equation is then solved by means of shooting method because the boundary conditions at the lift-off point are not fully sufficient. Several parameters such as cable diameter and initial tensile force are checked to study their effects on the balloon shapes. For a given material, the larger is the diameter of the cable, the higher is the air-drag coefficient on the cable, and the effect of the centrifugal force is weaker than that of the fluid resistance. Moreover, the maximum radius of the balloon and the total length of the control volume are small when the cable is thick.