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Abstract In this paper the analysis of the vertical motion prediction of six fast slender hulls using 2 ½ D high speed theory with cross-flow correction is presented. Experimental data for vertical motions in head sea are compared with five calculation cases where the cross-flow lift and drag coefficients are varied. The best fitting coefficient set is identified with reference to experimental data. The influence of slenderness ratio and ship speed is analyzed. Keywords Seakeeping; slender fast ships; cross flow; vertical motions prediction. Introduction The assessment of high speed craft seakeeping characteristics is important for several aspects of their design. Structure, general layout and passenger accommodation areas are strongly affected by ship motions. Cruising speed is connected to seakeeping performances.58405
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Optimization of the vessel for motion response is done at the design stage usually by means of prediction software. Most of the software used at design stage are based on 2-D strip theory with some corrections to take into account the forward speed. In the 3-D theories interaction along the hull is taken into account while the speed could be taken as a correction factor or could be implemented in the mathematical model depending how the free surface and body boundary conditions are satisfied. The latter method leads to better prediction especially for global loads but is very time consuming. Some effective hybrid methods have been developed. The one by Faltinsen and Zhao (1991) so called 2½ D high speed theory has been used in this work. All of them are based on the potential flow assumption i.e. the only damping forces will arise because the oscillating hull radiates waves away from ship. This offers great simplification in mathematical model without losing numerical accuracy for all motions except the roll. When dealing with high speed craft, the slenderness of hull is one of the factor used to reduce power requirements. For slender or very slender hull, the damping predicted by potential flow methods is so small that the damping forces relative to viscosity should be taken into account for any motion evaluation. Lee (1977), Chan (1992, 1993, 1995), Schellin (1995), Centeno (2000), Begovic (2002) and Davis (2003) have faced this problem using the cross-flow approach described by Thwaites (1960) for the aero profiles as a correction in vertical motions prediction. Their work was mainly concentrated on multihull configurations, while in this work the cross-flow approach was used for slender monohulls with advantage to investigate the sensitivity of cross-flow related phenomena without introducing further uncertainties as the interference among the hulls. In this paper the numerical assessment of heave and pitch in head sea for six hull forms with transom stern and round bilge is compared with experimental data relative to each hullform at different speeds. The calculations were performed using 2 ½ D high speed theory as implemented in VERES software and numerical code TRIM developed by author. Particular interest was put on the assessment of cross-flow coefficient values, usually considered equal to the values measured in aero profiles experiments in uniform flow. In this work, more appropriate values are proposed to better fit the experimental results. The sensitivity of final results to cross flow coefficients values as well as the influence of slenderness ratio is evaluated. Theory review We consider the ship as a rigid body travelling at the constant forward speed U. Furthermore, we assume that the rigid body will oscillate harmonically in time with six degrees of freedom with the complex amplitudes: ηj (j=1, 2..., 6), where j = 1, 2..., 6 refer to surge, sway, heave, roll, pitch and yaw respectively, as shown in the Fig.1. Figure 1. Motions, from VERES User's Manual We can write the motion equations as: () ( VjWjkk jk k jk k jk jk F F C B A M + = ⋅ + ⋅ + ⋅ + ∑ =61η η η & & & ) (1) where kη ,k η & and k η & & - displacement, velocity and acceleration respectively; Mjk - coefficients of mass matrix; Ajk - coefficients of added mass matrix; Bjk - coefficients of damping matrix; Cjk - coefficients of restoring matrix; WjF -wave-exciting force