Seagoing marine propulsion analysis in terms of main engine performance and fixed-pitch propeller hydrodynamics is an engineering problem that has not been exactly defined to date. This study utilizes an original and comprehensive mathematical approach—involving the approximate representation of one function by another—to define this problem in mathematical terms and solve it. This is achieved by imperatively applying an original and sophisticated hybrid combination of an existing, formidable and ingenious, mathematical methodology with different original comprehensive functional systems. These original functional systems approximately represent the operations of vessels under seagoing conditions, including the thermo-fluid and frictional processes of vessels’ main engines in terms of fuel oil consumption, as well as the hydrodynamic performance of the respective vessels in terms of the shaft propulsion power and the rotational speed of the fixed-pitch propellers driven by these engines. Based on the least-squares criterion, this original and sophisticated hybrid combination systematically attains remarkably close approximate representations under seagoing conditions. Apart from this novel exact definition in mathematical terms and the significance of the above original representations, this combination is also applicable for the approximation of the baselines demarcating the standard engineering context representing the ideal reference (sea trials) conditions, from the seagoing conditions.

The numerical algorithm used for the original multi-dimensional non-linear optimization analysis of the marine fixed pitch (screw) propulsion presented herewith, after its invention and publication has been widely used for the analysis and best fit (most probable / less uncertain) solution of over-determined non-linear mathematical problems, where the points of observations (measured data) are more than the unknown parameters in the mathematical formulation expressing the significant aspects of the observed phenomena. Any “local” attainable solution of this formidable and ingenious algorithm, may rely to the set of initial values of the unknown parameters, while not all possible solutions are expected to be physically significant for a specific problem, whereas judgment, bounds and testing are to be practiced for making sure that the attained solution is the best fit (most probable / less uncertain) one, and not necessarily the “global minimum” one. In the present paper the above algorithm is applied for the original analysis of standard ships propulsion, and particularly for the original combined application of thermo-fluid and frictional models of main engines, as well as of fixed pitch propulsion hydrodynamic models, necessary for resolving in an integrated manner the combined marine propulsion problem for standard ships under seagoing conditions.