Except for one point, at which should be the peak and  is predicted by POT, overall pitch prediction is best fitted by LIFT or α=0.035 - CD=0.25. At FN=0.8 heave experimental results are very well predicted by DRAG and by α=0.0 - CD=0.5. Pitch experimental results  are  significantly shifted on the left from  those  predicted  by  various calculations.  Regarding the absolute peak value, the POT prediction is the best one. with different H/λ in order to deal always with linear cases. The differences measured in heave and pitch responses in tests with various wave amplitudes are significant in the range of ωE= 1.8 &pide; 2.3 as can be seen in Diagrams 27 and 28. Regarding the heave, one H/λ case is best described by α=0.0 - CD=0.5 while the other one is best described by LIFT. Pitch results for the lower H/λ are very well fitted by POT. Higher H/λ results in the peak are quite underestimated by all of calculations performed, while in the higher frequency range they are converging to those relative to the lower H/λ.  CONCLUSIONS From the presented results it  can be seen that the high speed 2 ½ D potential theory highly overestimate the experimental data even in head seas for vertical motions for the considered slender hulls. The higher the speed is, the less realistic prediction will be. The correction of the obtained numerical results is identified in the cross flow effects. The five sets of the cross flow coefficient (α - CD) values were chosen and for all the considered models test cases were performed.  From the detailed analysis of the cross - flow coefficients it has been seen that at higher speeds (FN ≥0.5), the differences among performed calculations with different coefficient values become more significant.  Calculation using only potential flow method generally strongly overestimates the experimental results and calculation with  α=0.07 - CD=0.5 generally underestimates the experimental results. For the most of the considered models at higher speed, the predictions by α=0.07 - CD=0.0, by α=0.0 - CD=0.5 or by α=0.035 - CD=0.25 are very similar, and fit quite well the experimental data. Among these three coefficient sets no significant preference can be done. 源[自-优尔*`论/文'网·www.youerw.com
For physical exactness, it can  be considered that the case with drag coefficient without lift coefficient (α=0.0 - CD=0.5) is not physically founded. Only lift coefficient without drag was the approach used by Fang et al (1996). The set α=0.035 - CD=0.25 is giving very good prediction and as CD is non-linear function of relative fluid velocity (as can be seen in Formula 2) it can be interesting to consider it.   In the case of fuller hulls with L/B  ≤8, the potential theory can be considered sufficient for fair vertical motion prediction. For the slender ones, only viscous lift coefficient or the set  α=0.035, CD=0.25 could be considered sufficient for very good motion prediction.  These conclusions are consistent at all considered speeds, so it seems there is no significant changing in the trend with the velocity changing.  Acknowledgement Thanks to Prof. G. Boccadamo and P. Cassella from University of Naples Federico II and Prof. I.Zotti from University of Trieste for their assistance and support.  This work has been financially supported by University of Naples “Federico II” within the frame of 2003-2004 research program.  References Begovic, E (2002). "Cross-flow effects in the vertical motions prediction of fast slender ships", Ph.D. Thesis, University of Naples Federico II Begovic, E, and Boccadamo G, and Zotti I.(2002). "On The Effect Of Viscous Forces On The Motions Of High Speed Hulls", Proceedings of 3rd Int. Conference HIPER02, Bergen, pp 47-59 Blok, JJ, and Buekelman W (1984). "The High-Speed Displacement Ship Systematic Series Hull Forms - Seakeeping Characteristics ", Trans. SNAME, Vol 99, pp 125-150 Centeno, R, and Fonseca, N, and Guedes Soares C (2000). "Prediction of Motions of Catamarans Accounting for Viscous Effects, Int Shipbuilding Progress, Vol 47, No451, pp 303-323 Chan, HS (1992). "Dynamic Structural Responses of a Monohull Vessels to Regular Waves", Int Shipbuilding Progress, Vol 39, No419, pp287-315   Chan, HS (1993). "Prediction of Motions and Wave Loads of Twin-Hull Ships", Marine Structures, Vol 6, No1, 1993, pp 75-102 Davis, MR, Holloway DS (2003). "The Influence of Hull form on the Motions of High Speed Vessels in Head Sea", Ocean Engin, Vol 30, No 2, pp 91-115  Faltinsen, OM., and Zhao, R (1991). "Numerical Predictions of Ship Motions at High Forward Speed", Phil Trans Royal Society, London, Vol 334, pp 241-252 Fang, CC, and Chan, HS, and Incecik, A (1996). "Investigation of Motions of Catamarans in Regular Waves - parts I and II", Ocean Engineering, Vol 23, No1, pp 89-105 Keuning, JA (1990). "Distribution of Added Mass and Damping Along the Length of a Ship Model Moving at High Forward Speed", Int Shipbuilding Progress, Vol 37, pp 123-150 Lee, CM, and Curphey, MR (1977). "Prediction of Motion, Stability and Wave Load of Small-Waterplane-Area Twin-Hull-Ships", SNAME Trans, Vol 85, pp 94-130 Molland, AF, and Wellicome, JF, and Temarel, P, and Cic, J, and Taunton, DJ (2000) "Experimental Investigation of the Seakeeping Characteristics of Fast Displacement Catamarans in Head and Oblique Seas", RINA Trans, Vol 142 Schelin, TE, and Rathje, H (1995). "A Panel Method Applied to Hydrodynamic Analysis of Twin-Hull Ships", Proc of 3rd Int Symposium FAST 95, Lübeck–Travemünde, pp1017-1030 Thwaites, B, (1960). "Incompressible Aerodynamics", Oxford University Press, 1960 MARINTEK - Sintef Group: VERES Version 3.18 - User's Manual, January 1998  横向流作用下瘦长船体的垂直运动预测英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_63319.html