Stability of Towed Arrays

Towed arrays are common in both aeronautical and maritime applications.  But despite their long history, not all arrays (or array elements) behave in a predictable manner.  By way of example, the U.S. Navy’s Low Frequency Active Array (LFAA) experiences excessive contact damage when towed in certain sea states.  Attempts have been made to identify the responsible design attributes using linear motion simulators, but have never predicted element motions large enough to cause damage.  It is therefore speculated that non-linear effects or coupled-motions are responsible for larger than expected forces. 

Quantifying these forces for building a motion simulator usually requires testing with a Planar Motion Mechanism (PMM).  But in this case the number of combinations of non-linear and/or coupled terms is far too great.  RANS was therefore used exactly like a PMM.  Isolated LFAA elements were forced in a wide range of motions, and time histories of the resulting 6 Degree-Of-Freedom (DOF) forces recorded.  Prescribed motions include single DOF’s with varying amplitudes and frequencies (to look for non-linearities), and multiple DOF’s with varying motion phases (to study coupling).  The embedded movie shows velocity in the wake of one of the coupled motion simulations (roll plus sway).  Prescribed motion starts slowly, but force histories are only analyzed once a statistically stationary state is reached. 

Once all force histories are available, system identification techniques are used to devise relationships between 6-DOF motions and 6-DOF forces.  Both velocity-dependent and acceleration-dependent force models are developed, and the resulting relationships coded into existing motion simulation programs.  The new simulators can now be trusted to properly account for non-linearities in amplitude and frequency, as well as to accurately resolve any complexity due to coupled motion.