Parametrically Excited Transverse Plane Instabilities on High-Speed Planing Hulls.

Abstract

Planing hulls sometimes exhibit dynamic instabilities, endangering the safety of passengers and crew. Most of the efforts in understanding these phenomena have concentrated in the vertical plane (e.g., porpoising). Little has been done in the horizontal plane, where the emphasis has been placed in the understanding of progressive heeling. The physics and conditions under which planing hulls will develop oscillatory roll instabilities (e.g., chine walking) are still not well understood and therefore there are not accepted guidelines to prevent them. Consistent with this need of understanding, in this research a method for investigating the conditions under which high-speed planing hulls can exhibit large oscillatory roll motions parametrically excited by small heave and pitch motions is proposed.

A one-way coupling between heave-pitch and roll is assumed, and the roll equation of motion is written as a Hill's equation with third order non-linearities. The stability boundaries in the Ince-Strutt diagram are obtained, the influence of the different terms in the roll equation of motion on these boundaries is discussed, and conditions to be satisfied in order to avoid large amplitude periodic roll motions in the vicinity of the principal parametric resonance are derived.

In order to reduce the coefficients for the roll equation of motion, the generalized forces and moments acting on a planing hull in asymmetric conditions are obtained by the 2D+t approach. Non-linear models are proposed for roll added mass and roll damping, based on Fourier analysis of the roll moment time series. It is shown that the presence of a third order harmonic of different sign than the first order harmonic in the out-of-phase component reduces the linear roll damping, increasing the probability of parametric roll.

Lastly, two of the conditions tested by Judge at the United States Naval Academy are used as case studies. The results show that high-speed planing hulls running at low mean wetted length and low trim are more prone to develop parametric roll than planing hulls running at high mean wetted length and high trim. This is consistent with what is observed in the field where lightly loaded high-speed planing hulls sometimes exhibit "chine-walking".