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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line PREDICTION OF WAVE PRESSURE AND LOADS ON ACTUAL SHIPS BY THE ENHANCED UNIFED THEORY 381 Fig. 10 Torsional moment at S.S. 7 of a container ship (Fn=0.215) With this expectation, EUT was applied to a VLCC tanker model and a recent container ship model, and computed results were compared with experiments to confirm applicability of the theory. However, the results were not so good as expected before starting this study. One important reason of this is that the prediction of ship motions is not improved so much when compared to the results of STFM, since the ship motions are influential in the prediction of the wave pressure and resulting wave loads. Of course, the effects of nonlinearity and three-dimensionality of the flow may be important particularly around the bow part, and viscous effects are also important near the stern. These effects must be accounted for by more sophisticated 3-D computation methods. However, EUT is still advantageous from a practical viewpoint, because it is efficient in computations. Further study is needed for precise prediction of the ship motions, for which the forward-speed effects on the free-surface condition must be taken into account in a more rigorous way. ACKNOWLEDGMENTS The authors would like to thank Mr. H.Sueoka and Dr. T.Kuroiwa of Mitsubishi Heavy Industries for their help in the course of the present study. Mr. Y.Tozaki in assisting numerical computations is also greatly acknowledged. REFERENCES Kashiwagi, M., “Prediction of Surge and Its Effects on Added Resistance by Means of the Enhanced Unified Theory,” Transactions of West-Japan Society of Naval Architects, No. 89, 1995, pp. 77–89. Kashiwagi, M., “Numerical Seakeeping Calculations Based on the Slender Ship Theory,” Ship Technology Research, Vol. 4, No. 4, 1997, pp. 167–192. Kashiwagi, M., Kawasoe, K. and Inada, M., “A Study on Ship Motion and Added Resistance in Waves (in Japanese),” Journal of Kansai Society of N. A., Japan, No. 234, 2000, in press. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line PREDICTION OF WAVE PRESSURE AND LOADS ON ACTUAL SHIPS BY THE ENHANCED UNIFED THEORY 382 Newman, J.N., “The Theory of Ship Motions,” Advances of Applied Mechanics, Vol. 18, 1978, pp. 221–283. Salvesen, N., Tuck, E.O. and Faltinsen, O.M., “Ship Motions and Sea Loads,” Transactions of SNAME, Vol. 78, 1970, pp. 1–30. Sclavounos, P.D., “The Diffraction of Free-Surface Waves by a Slender Ship,” Journal of Ship Research, Vol. 28, No. 1, 1984, pp. 29–47. Sclavounos, P.D., “The Unified Slender-Body Theory: Ship Motions in Waves,” Proceedings of the 15th Symposium on Naval Hydrodynamics, Hamburg, 1985, pp. 177–192. Tanizawa, K., Taguchi, H.Saruta, T. and Watanabe, I., “Experimental Study of Wave Pressure on VLCC Running in Short Waves (in Japanese),” Journal of Society of Naval Architects, Japan, No. 174, 1993, pp. 233–242. Fig. 11 Vertical bending moment at S.S. 5 of a container ship (χ=180°) the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line PREDICTION OF WAVE PRESSURE AND LOADS ON ACTUAL SHIPS BY THE ENHANCED UNIFED THEORY 383 DISCUSSION P.Sclavounos Massachusetts Institute of Technology, USA I would like to congratulate the authors for a series of thorough studies, including the present one, refining the unified slender body theory for the prediction of motions and wave induced loads of realistic ship hulls. I would like to commend the authors' diligent refinement of the theory and its validation against careful experimental measurements. It is the experience the authors are reporting that has led me to switch my energies since the mid 80's to the development of the 3D Rankine Panel Method SWAN. I am however very pleased to see that several of the shortcomings of the unified slender body theory with forward speed have been removed by the authors. I have a few comments and questions to which I welcome the authors' response: The good correlation of STFM and EUT for the motions of the tanker is probably due to her low Froude number. It would be interesting to see how both methods perform at U=0. We have seen some very good performance of unified theory in that limit which seems to be corroborated by the results the authors present. In our experience with SWAN, one of the most important forward speed effect arises from the careful and complete treatment of the m-terms on the body boundary condition. These terms may actually be computed from the double body flow without the need to model surface wave disturbances. Their evaluation would require the use of a 3D panel method, yet their values can be input into EUT as forcing terms in the body boundary condition. It would be interesting to see the effect of this “experiment” on the performance on the EUT. It has been our experience that the m-terms in the body boundary condition contribute much more significant forward speed effects than their counterpart on the free surface condition, as the authors appear to suggest. What is the behavior of the EUT near the τ=1/4 singularity in quartering waves. It is my recollection that the unified theory solution developed in the late 70's and early 80's by Nick and myself was predicting a singularity in the motion predictions at τ=1/4. We have since seen that this singularity is not really present in SWAN, yet it remains difficult to resolve. How does EUT deal with this delicate regime when it arises in your computations and experiments? AUTHOR'S REPLY 1) Concerning good performance of EUT in the limiting case of U=0, we have shown many supporting results not only for a single body in open sea but also the tank-wall interference and catamaran problems (see reference [A1]). From theoretical viewpoint, the unified theory is a perfect one in the framework of slender- body theory. 2) Regarding the effect of the steady disturbance in the body boundary condition, our recognition seems to be different from that of discussor. Firstly, our purpose is to develop a practical calculation method which must be easy to implement but reliable in the design stage. Secondly, the results of the radiation forces (especially the diagonal coefficients) by the present method are in good agreement with experiments. Recent results for modified Wigley model with L/B=6.67 are shown in reference [A2]. The degree of agreement by means of EUT is almost perfect in A33, B33, and A55. The results of High-Speed Slender-Ship Theory (HSSST) are also shown in reference [A2] and HSSST gives obvious improvement in B55. This tendency is much more prominent in the cross-coupling terms. HSSST uses also the uniform flow assumption in the body boundary condition, but the forward-speed effects in the free-surface condition are fully taken into account. In fact, we have learned from Rational Strip Theory (RST) of Ogilvie & Tuck that the forward-speed effect in the free- surface boundary condition is important in the cross-coupling terms, which improves clearly over the strip theory. HSSST encompasses RST, and thus it is natural to see good agreement with experiments. From experiences mentioned above, we suggest that the forward-speed effects in the free-surface condition may be more significant than the effects of disturbance potential in the the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line PREDICTION OF WAVE PRESSURE AND LOADS ON ACTUAL SHIPS BY THE ENHANCED UNIFED THEORY 384 body boundary condition. 3) As shown in some figures in references [A1] and [A2], EUT shows singularity at the frequency equal to τ=1/4, and experimental data also show rapid variation near τ=1/4. I suppose the results of SWAN are imperfect near τ=1/4, and we cannot discuss this sensitive behavior with questionable numerical results. [A1] M.Kashiwagi (1997); Numerical Seakeeping Calculations Based on the Slender Ship Theory, Ship Technology Research (Schiffstechnik), Vol. 4, No. 4, pp. 167–192. [A2] M.Kashiwagi (2000); The State of the Art on Slender-Ship Theories of Seakeeping, Proceedings of the 4th Osaka Colloquium on Seakeeping Performance of Ships, October, 2000. the authoritative version for attribution.