Numerical Solutions 



further inquired whether constraints on the coefficients are needed to represent 

 ship sections. The author replied that advantage had already been taken of the 

 symmetry of the ship sections, as a consequence of which only odd powers and 

 real coefficients occurred in the series form of the transformation, and that, 

 because the series was convergent, the only restriction on the number of terms 

 was that of numerical accuracy. 



Dr. Timman (Delft Technological University, Netherlands) asked whether 

 the high degree of accuracy sought in the representation was desired for the 

 purpose of laying out ship lines or for use in calculating added mass and damp- 

 ing coefficients. The author agreed that, for the latter purpose, high accuracy 

 of representation is not required, but wavemaking resistance is sensitive to 

 small variation in form. 



Since the parametric form consists essentially of expansions in Fourier 

 series. Dr. Eggers (Universitat Hamburg, Germany) was concerned that slopes 

 might not be accurately reproduced. The author's experience is that appreci- 

 able deviations occur only near corner points which are necessarily rounded 

 by a truncated Fourier series. He felt, however, that it was preferable to ac- 

 cept a slight rounding of corners than to include the mathematical form of the 

 branch-point transformations in the equations of the ship hull. 



Finally Dr. Barakat described his recent work on the heaving of a semi- 

 immersed cylinder of arbitrary section on a free surface in water of finite depth 

 in which the added mass and damping coefficients were determined in the 

 presence of an incident wave. He found that the modified values of these coeffi- 

 cients, the so-called dynamical added- mass and damping coefficients, make a 

 tremendous difference in the ship response. Thus, contrary to the previous 

 discussion on the insensitivity of the added mass and damping coefficients, the 

 dynamical response of a cylinder is quite sensitive to the shape of section. 



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