In this paper, we describe longitudinal stability of a supercavitating underwater vehicle with planing. First, cavity dynamics were modeled to obtain the cavity profile for calculating the wetted area. Subsequently, the forces and moments acting on each wetted part of the vehicle---the cavitator, fins, and vehicle body---were obtained by dynamics modeling. The longitudinal stability of the nonlinear dynamics is analyzed through the phase portrait of pitch angle/pitch rate based on steady state dynamics. Numerical simulation shows that the supercavitating vehicle can maintain pitch angle in the presence of planing force and can follow the given depth command.
A supercavitating underwater vehicle can flight at much faster speed than conventional underwater vehicle by eliminating frictional drag with bubble called cavity, which is enveloping the whole vehicle body. Most of the supercavitating underwater vehicle maintain the stability using control fin located in the vehicle transom. Without the control fin, a planing is necessarily generated, and the planing force causes sudden change in the vehicle attitude, thereby degrading stability.
Many scientists have studied dynamics and control of a supercavitating vehicle (Dzielski and Kurdila, 2003; Hassouneh et al., 2013; Kirschner et al., 2002; Li et al., 2008; Mao et al., 2015; Nguyen and Balachandran, 2011; Sanabria et al., 2014; Shao et al., 2003; Vanek et al., 2007). Most studies, however, minimize the occurrence of planing or control it using control fin. There is no research to control the vehicle without using control fin.
In this study, we focus on the stability of a supercavitating underwater vehicle with planing. First, we construct equation of motion of the supercavitating vehicle and the forces acting on the vehicle is defined. The longitudinal stability of the nonlinear equation of motion was analyzed based on the phase portrait of pitch angle/pitch rate using steady state dynamics. The control gain was estimated based on steady state phase portrait results, and unsteady numerical simulation was performed to determine whether the planing supported vehicle can follow the given depth command.