SIMULATION AND NONLINEAR DYNAMICS ANALYSIS OF PLANING HULLS

The high speeds, small trim angles, and shallow drafts of planning hul ls produce large changes in vessel wetted surface which, in turn, lead to significant hydrodynamic and dynamic nonlinearities. Due to the co mplex nonlinearities of this type of craft, naval architects and plani ng boat designers tend to rely upon experimental tests or simulation f or guidance. In order for simulation to be an effective design tool, a fundamental understanding of the system's dynamic characteristics is required. This paper describes a developing methodology by which the n ecessary insight may be obtained. A demonstration of the combined use of modern methods of dynamical system analysis with simulation is give n in the evaluation of the vertical motions of a typical planing hull. Extending the work of Troesch and Hicks (1992) and Troesch and Falzar ano (1993), the complete nonlinear hydrodynamic force and moment equat ions of Zarnick (1978) are expanded in a multi-variable Taylor series. As a result, the nonlinear integro-differential equations of motion a re replaced by a set of highly coupled, ordinary differential equation s with constant coefficients, valid through third order. Closed-form, analytic expressions are available for the coefficients (Hicks, 1993). Numerical examples for all first-order and some second-order terms ar e presented. Once completely determined, the coefficient matrices will serve as input to path following or continuation methods (e.g., Seyde l, 1988) where heave and pitch magnification curves can be generated, allowing the entire system response to be viewed. The branching behavi or of the solutions resulting from a variation of the center of gravit y is examined in detail. These studies of the second-order accurate mo del show the potential of the method to identify areas of critical dyn amic response, which in turn can be verified and explored further thro ugh the use of the simulator.