SIMULATION MODELING OF FLIGHT DYNAMICS, CONTROL AND TRAJECTORY OPTIMIZATION OF ROTORCRAFT TOWING SUBMERGED LOADS
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This work presents the mathematical modeling and analysis of helicopters towing submerged loads using long cables for sub-surface object detection when surface-based vessels cannot operate safely. A geometrically exact model of rotating beams is derived, and used to represent both the cable dynamics and rotor blade dynamics. Flight dynamics and trim conditions for an axially flexible straight cable and a curved cable are separately formulated for a general case of helical climbing turns, and used to cross-validate each other. In steady flight, the trim longitudinal dynamics of the submerged load produces down-forces from towed body fins, increasing the apparent weight of the tow system. Cable and towed body drag manifest as increases in the effective equivalent flat- plate area, necessitating excessive nose-down helicopter trim pitch attitudes (-6◦ ) and causing pilot discomfort. Excessive pitch attitudes can be avoided using aft offset of the helicopter tow point, or the deployment of longer cables in combination with pitching fins to regulate towed body depth. In steady level turning flight, cable and towed body drag result in the submerged load turning with a consistently smaller radius than the helicopter. Depth regulation in turning flight using pitching fins is less effective than in forward flight due to increased cable drag opposing larger down-forces. Analysis of linearized models showed that the helicopter frequency response to pilot inputs is unaffected by the addition of the cable and towed body above 1 rad/s. The low-frequency response magnitude reduces with increasing hydrodynamic drag on the cable and towed body, and is unaffected by cable structural properties due to over-damped stabilization from hydrodynamics. The swashplate inputs required to guide the towed body along a "tear-drop" shaped trajectory are obtained using a two-stage process. The motions of the tow point that guide the submerged load along the target path are obtained using an optimization process. The system target states are generated based on these tow point motions, and an LQR controller is used to guide the helicopter along its target path. Trim rotor inflows from the vortex wake model are obtained at the various equilibrium points used to construct helicopter target states, interpolated and applied as "delta" corrections to the dynamic inflow model. Blade elastic twist has a significant effect on rotor power predictions and the steady hub loads, while flap bending elasticity acts as a vibration absorber to attenuate the oscillatory component of hub rolling and pitching moments.