The Mathematical Model of Hydrodynamic Forces Acting on Ship Moving in an Oblique Direction with Fluid-dynamic Concepts (2nd Reports)

Abstract

The authors had pursued the mathematical model of hydrodynamic forces acting on ships moving in an oblique direction. This model could separate the fluid force from the following forces; ideal force (Munk moment), lift and induced drag forces due to viscosity, cross flow drag and lift forces, as well as the frictional drag force. In the paper referred to above, the mathematical model had a good agreement with measured forces and gave the physical meanings in terms of fluid dynamics. However, in some cases the model could not describe the stall effects with reasonable physical meanings in terms of fluid dynamics. This occurred in the case where the stall effects decreased the lift effect and did not start in the stage of small drift angles. In order to solve this problem of unreasonable stall effects, this paper adopted the cross flow drag coefficient C_D=C_<D90>・&mid;sinβ&mid;・(1+P・cos^2β) instead of C_D=C_<D90>・&sim;sinβ&sim;, and analysed forces mainly using longitudinal force when taking into account of reasonable stall effects in stead of the lateral force. As the result, the authors generated the following mathematical model. [numerical formula] where [numerical formula] and U:ship spped u':longitudinal component of speed (=u/U=cosβ) without dimension v':lateral component of speed (=v/U=-sinβ) without dimension m'_x,m'_y:added mass coefficients without dimension C'_<LAB>:coefficient of lift force due to ship's fore-aft asymmetry C'_F:coefficient of longitudinal resistant force C'_L:coefficient of viscous lift force C'_<Di>:coefficient of induced drag force ΔC'_L, ΔC'<Di>:coefficients of stall C_<D90>':coefficient of cross flow drag at β=90°l_<v0>:longitudinal center of viscous lift force from midship l_<i0>:longitudinal center of induced drag force from midship p:anothecoefficient of cross flow drag m'_0, m'_1:moments of lateral projected area of ship about midship