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In this paper some analytical developments concerning the possibility of generating a rectilinear motion of vessels subject to vibration, without the use of propellers (see Muscia and Sciuto 2009, 2010, Muscia 2014) are presented. The motion is obtained by a device equipped with counter rotating masses installed in the boat which vibrates along the longitudinal direction. The hull has a suitably shaped stern. The study considers an analysis for evaluating the energy that the propulsion system consumes in relation to its performances. A further objective was to maximize the speed of the system while keeping certain parameters unchanged relating to the equations of motion of the device and suitably allocating the counter rotating masses. This result is obtained by using elliptical gears to transmit the motion from the driving motor to a double or more pairs of counter rotating masses. This solution allows one to reach the variability of the angular velocity of the counter rotating masses during each revolution in accordance with certain laws that maximize the thrust applied to the vessel preferentially along a direction in respect of the opposite one, all being equal. The previous studies [Muscia and Sciuto (2009,2010)] considered only one pair of counter rotating masses that rotated with constant angular velocity. In the conclusion of this first part of the work, a formulation to compute the propulsive efficiency of the device study is defined.