When an automatic course keeping is introduced, as is quite popular in modern navigation, the closed-loop control system consists of autopilot device, power unit, steering gear, ship dynamics, and magnetic or gyrocompass. We derive mathematical models of each element of the automatic steering system. We provide a method of theoretical analysis on the propulsive energy loss related to automatic steering of ships in the open seas, taking account of the on-off(non-linear) characteristics of power unit. Also we paid attention to non-linear element installed in autopilot device, which is normally called weather adjuster. Next we make numerical calculation of the effects of autopilot control constants on the propulsive energy loss for two kinds of ship, a fishing boat and an ore carrier. Realistic sea and wind disturbances are employed in the calculation.

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