The coupled heave and pitch motions of hull forms with flare and overhangs are examined numerically. The presence of flare and overhangs is numerically modelled with nonlinear hydrostatic and Froude-Krylov forces based on integrals over the instantaneous wetted surface. Forces due to radiation and diffraction are computed with a linear strip-theory. These forces are combined in two coupled nonlinear differential equations of motion that are solved in the time domain with a fourth-order Runge-Kutta integration method. An assessment of the impact of flare and overhangs on motions is obtained by comparing these nonlinear solutions with solutions of the traditional linear equations of motion, which do not contain forces due to flare and overhangs. For an example based on an International America's Cup Class yacht design, it is found that the nonlinear heave and pitch motions are smaller than the linear motions. This is primarily due to reduced first-order response components, which are coupled with nonlinear response components. Comparisons of these results with towing tank data demonstrate that the nonlinear procedure improves prediction quality relative to linear results. In support of this numerical work, the hydrostatic and FroudeKrylov force integrals are expanded in Taylor series with respect to wave elevation. These results indicate how hydrostatic and Froude-Krylov forces change with changing flare and overhang angles, revealing that sectional slope has second and third-order effects on forces while sectional curvature and overhang angles produce third-order effects.
The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas
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Kuhn, John C., and Eric C. Schlageter. "The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas." Paper presented at the SNAME 11th Chesapeake Sailing Yacht Symposium, Annapolis, Maryland, USA, January 1993. doi: https://doi.org/10.5957/CSYS-1993-003
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