Linear and nonlinear analyses of the porpoising dynamics of high-speed planing craft using full-scale trial data

Abstract

Although it is known from previous studies that porpoising in high-speed planing craft is a Hopf bifurcation, this study examined its occurrence and disappearance using the motion model identified from full-scale test data. Herein, we first analyzed the stability of the system linearized near the equilibrium point. From its results, we reconfirmed the knowledge that porpoising occurs when the system becomes unstable in the vicinity of the equilibrium point. We also found that the system became unstable as the thrust or trim angle of the outboard motor decreased. This finding was consistent with the results of a full-scale craft test performed in a previous study. Second, we confirmed that the limit cycle which is a result of the nonlinearity of the system was stable. The two analyses indicate that porpoising corresponds to the supercritical Hopf bifurcation. Furthermore, in the vicinity of the bifurcation point, it was found that stable equilibrium points and stable limit cycles can coexist. Finally, we confirmed this phenomenon in the full-scale test.