Considering the simplified vortex model with ring, horse-shoe and 3D cross-flow vortex described in the authors' previous papers, the authors presented as component type mathematical model for hydrodynamic forces X, Y, N that act on a steered hull with an even keel. The mathematical model can estimate the hydrodynamic forces in turning motion by using the hydrodynamic characteristics analyzed even from oblique hydrodynamic forces through the model, and additionally describe the hydrodynamic forces in maneuvering motion with small to large yaw rate and drift angle. This paper describes the mathematical model due to the simplified vortex system for the trim condition in general, such as in sea trials of cargo ships for IMO regulation and the conventional stage of fishing vessels with initial trim. Furthermore this paper presents a method for analyzing the characteristics of oblique hydrodynamic forces from the new viewpoint of measuring system with 2 support points at FP and AP. This mathematical model can describe most characteristics of the hydrodynamic forces in oblique motion with drift angle 0 to 90 degree and turning motion with yaw rate |γ'|≤1, by using the hydrodynamic characteristics analyzed even from oblique hydrodynamic forces with drift angle covering 020 degree.