Preliminary calculations for a flexible cable in steady, non-uniform flow

Podeʼs closed-form solution provides the shape and tension within a flexible cable tethered to a balloon or buoy subjected to a steady, two-dimensional uniform current. When the flow is non-uniform, the velocity field must be decomposed into an approximate step-wise (“polygonal”) distribution, and a starting point for the calculations assumed. A simple and robust solution methodology is proposed which discretizes the cable and employs static equilibrium of each element and an optimization technique to determine the shape and tension for the cable. A parametric study revealed that the proposed model agreed exceptionally well with Podeʼs closed form solution for uniform velocity distributions in both tension and position, even with a small number of elements. Excellent agreement was obtained for tension between all three methods. For a non-uniform velocity field, cable shape and tension are calculated; no closed-form solution was available for comparison in this case. Positions predicted by the polygonal method approached those obtained by the proposed model, but only with an order of magnitude more elements than with the proposed method; agreement in tension was excellent. The model has also been applied to multiple balloons, and, by changing the fluid medium, may be readily extended to water buoys.