To improve the formulation of ship–ship interaction forces and moments in a mathematical model of a ship maneuvring simulator, we developed a new generic mathematical model for the overtaking maneuver. This process involves using the numerical results, which provide a potentially complete set of data from which (within the constraints of the numerical modelling) everything necessary can be acquired. We found that the new generic mathematical model is as accurate as the numerical model. It is also more accessible to a navigator, master, or pilot, who could use it on a palmtop computer by keying in a few numberical estimates of the size, position, and speed of the neighboring ship and receive almost instant aneous results, giving time for a refined strategy to be validated if necessary. These results can also readily be used by simulation program developers to simulate the worst possible scenarios.