Nonlinear slender-body approach for predicting planing hull performance

The slender body approach with a nonlinear free surface boundary condition is used in order to numerically solve a boundary value problem which defines the two-dimensional velocity field surrounding the cross section of a planing tetrahedral. A coordinate system transformation is applied so that the sectional problem appears as two inclined plates connected at their apparent trailing edges planing away from the centerline in opposite directions. An infinitely long spray jet is attached to the cross section's inclined wall, and the nonlinear free surface is iteratively matched between the horizontal free surface at the far field and the near field elevated free surface which ends as an attached spray jet.;A special reduction of the free surface dynamic and kinematic conditions allows us to represent the nonlinear free surface by a constant vortex distribution. Along the centerline, a semi-infinite distribution of constant negative sources are placed. The unknowns are the vortex distribution along the sectional contour and the position of the free surface. Successive numerical solutions of the related boundary value problem are performed while the free surface position is iteratively modified. The numerical scheme is convergent and a smoothly curved free surface satisfying the boundary conditions, is well-defined.;The sectional pressure, which is calculated by using the solution vector of vortex distribution along the sectional contour, is integrated longitudinally in order to express the total lift and drag forces acting on the slender hull.