Physical analysis methods for planing hull turning circles

In the present study, an analysis method is proposed for the steady turning circles of high-speed small craft using the circular motion equations and applying force and moment balances with multiple coordinate systems. Multiple coordinate systems are necessary since multiple components of forces, moments, and motions are created and coupled during turning. The horizontal ship-fixed and cylindrical coordinates are used to derive the circular motion equations, with the forces and velocities projected to the horizontal ship-fixed system to calculate the drift angle, centrifugal force, and speed loss. The proposed method is applied to analyze the results for both a displacement hull and a high-speed planing hull. For the displacement hull, the force balances in the ship-fixed and horizontal ship-fixed systems are very similar due to the negligible roll and pitch angles. For the planing hull with different steering angles, the sway forces show very different trends in different coordinate systems. The dominant force component differs with different hull forms and steering angles in the ship-fixed system, but is the same in the horizontal ship-fixed coordinate system. The differences in heel angle signs for the displacement hull and planing hull have been explained. It should be recognized that the analysis methods presented herein can also be useful to other researchers using their own experimental and/or CFD data to reach similar beneficial results and conclusions.