Transverse motions of a single sphere in hanging or swing configurations under a longitudinal flow

As a result of the reporting of casual observations of the oscillation or rotation of the beacons in transmission line guard cables, some attention has been paid to the stability of the guard cables with beacons.

The relatively more frequent observation of these motions has been explained in recent papers dealing with the elastic part of the problem as a consequence of the increasing number of resonant frequencies (one for each additional beacon) that can be excited by appropriate aerodynamic loads. But a model that could explain the aerodynamic forces that can give rise to this motion is still lacking.

In this paper we consider the transverse motions of a single sphere in two simplified configurations, (1) hanging (tethered at one point), and (2) swing (tethered at two points) under a longitudinal flow, performing small amplitude swinging oscillations or circular-orbit autorotation about an axis parallel to the main flow direction. The dynamic model here presented is based on the motion equations, which also include a model for the aerodynamic lift and drag forces on the sphere in transverse motion, which considers the effect of changes of flow around the sphere due to the cable interference. These forces are contained in the symmetry plane of the flow relative to the sphere, and, when projected on the lateral direction, give rise to a lateral force, which can explain the existence of the azimuthal motion even at a large reduced velocity, outside the vortex induced vibration (VIV) range The conditions for stable small oscillation motion and circular-orbit autorotation of a sphere in a swing configuration are given.

The results for the aerodynamic loads in transverse motion have also been applied to the case of a circular-orbit autorotation of a hanging sphere (spherical pendulum) under a vertical flow. The angular rotation speed and the orbit radius (or cable angle) have been determined as a function of aerodynamic coefficients and configuration parameters.