Modeling and Simulation of the 6 DOF Motion of a High Speed Planing Hull Running in Calm Sea

When a planing hull straightly runs and turns, its floating position and pitch angle are changed depending on its speed, and large transient motion happens. In this paper, six degrees of freedom(6 DOF) equations of motion, which could simulate the motion of a planing hull, are established. Static and dynamic forces in vertical plane are modeled using pre-calculated displacements and metacentric heights depending on various draft, lift under bottom, and vertical damping coefficients which are used to tune the final motion. Hydrodynamic coefficients in horizontal plane at various equilibrium state are calculated by using Lewandowski's empirical formula and the speed-dependent equilibrium state are calculated beforehand by Savitsky's formula. The speed effects are considered by curve-fitting the coefficients at various speed to the polynomials. Accelerating, decelerating and backing, turning, and zig-zag are simulated and compared with the sea trial results, and it is confirmed that the speed reduction, roll, and pitch during such maneuvers of sea trial and simulation are well consistent.