A comparison of the analytical, numerical, and experimental solutions to the classic dangling chain problem

The incorporation of trailing wire antennas in military aircraft has been the result of unique mission requirements of HF (High Frequency), LF (Low Frequency), and VLF (Very Low Frequency) strategic communications. The complex physical dynamics of these trailing wires necessitate accurate modeling in order to determine the unique characteristics associated with trailing wire antennas. Accurate modeling of trailing wires stems from the need to determine the time dependent cable wire shape with respect to aircraft maneuvers and/or environmental characteristics that produce direct forces to the trailing wire. The knowledge of wire shape with respect to various input forces will therefore result in practical engineering solutions to limit the adverse effects caused by such forces. As an invaluable instructional tool for the development of dynamic models of trailing wires, the fidelity of lab experiments that correlate with both the analytical and numerical modeling of complex physical systems are essential for complete understanding. This thesis demonstrates the close correlation possible for the classic dangling chain problem. A full appreciation model of the governing equation for the classic dangling chain problem with a dead weight attached to the end was developed and solved analytically. The analytical solutions were then used to validate the solutions found in the numerical simulation and actual experiment. The solutions were then compared to determine the utility of using applied numerical and experimental techniques for solving the dangling chain governing equation. Comparison of the solutions demonstrated the close correlation of simple experiments with both the analytical and numerical models of physical dynamic systems that can provide a robust instructional tool in the development of trailing wires in military aircraft.