Porpoising is a well-known longitudinal stability failure mode of the high-speed planing craft. The inception of porpoising was firstly theoretically predicted for conventional planning vessels and it involves periodic, coupled heave-pitch oscillation motion. Similarly, it possibly happens for M-hull planing craft at high speeds. Based on coupled heaving-pitching motion equations, the longitudinal stability is judged by Routh-Hurwitz criterion. By analyzing on the characteristic solution of motion equations, in this research, longitudinal motion is firstly divided into three motion modes: steady motion, sustained amplitude oscillatory motion and increasing amplitude motion. To investigate these three motion modes, a comprehensive series of dynamic CFD simulations have been performed in the case of single and double M- hull planing craft with different longitudinal positions of gravity center, pitching radius of inertia and forward speeds. Unsteady Reynolds Average Navier-Stokes equations (URANS) are solved based on finite volume method (FVM) and SIMPLE algorithm. The rigid motion is simulated by DFBI module and overset grid technology and the free surface is captured by VOF method. In this series of numerical simulation, 2-DOF motions of direct navigation in calm water for both single and double M-hull planing craft are carried out. By dealing with heave and pitch motion curves, the distribution of these three motion modes and the limit of motion stability are presented. The limit curves of dynamic stability for both M and DM are also given. By comparison, M-hull planning craft has relatively optimum pitching radius of inertia which results in better performance of motion stability and M has a wider range of sustained amplitude oscillatory motion than DM.
An M-hull ship can be considered as the combination of a conventional planing craft, a multi-body high-speed ship, a microbubble drag reduction ship and a hovercraft. According to the shape of its transverse section, similar types are brought forward and one of them is double M-hull planing craft. The transverse profile and 3-D views of single and double M-hull planing craft are as shown in Fig1.
