Wave Excitationless Ships Forms 



This transform has been used by myself and others for other purposes, and with 

 the proper choices of the coefficients a. and the number of coefficients, this can 

 also generate more or less smooth bulbous sections which display the particular 

 hydrodynamic behavior of interest here. The hydrodynamic coefficients for these 

 transform sections in forced vertical, horizontal, or rolling motion in fluid of 

 arbitrary depth can be calculated exactly (in the numerical technique sense) by 

 the methods I have previously used. The point is that exact procedures of anal- 

 ysis of continuous shiplike forms tend to confirm the results of the authors' ap- 

 proximate calculations for their forms. 



As an example, I have results for a family 

 of forms illustrated in Fig. Dl. The family 

 varies strut length and strut width. The geo- 

 metric coefficients a. were found by a proce- 

 dure numerically mapping the offsets of bulbuous 

 shapes selected as a family. The form with 

 the widest strut, section 1, with the beam of the 

 strut equal to the beam of the bulb, that is, the 

 form with vertical sides and without reverse 

 curvature, does not show zero vertical force 

 in the finite frequency range. The other forms 

 show the desired phenomena and the critical 

 frequencies; and, as a family, the trend of be- 

 havior is smooth. For clarity of the figures, 

 I have illustrated the wave amplitude ratio A 

 (Fig. D2) and the free surface correction coef- 

 ficient k^ (Fig. D3) for only three of the forms. 

 The zeroes of generated wave amplitude are 

 easily seen. The approximate zero wave- 

 excitation according to the estimate by the 

 authors is not obvious in my figures, but it is 

 clearly dependent on the added mass coeffi- 

 cient, and its variation with frequency is dis- 

 played by the free-surface correction coef- 

 ficient. 



Unfortunately, I can only report these the- 

 oretical observations without further experi- 

 mental results such as the authors have re- 

 ported. On this note, I will close with repeated 

 congratulations to the authors for both the the- 

 oretical estimate and experimental report. 



6 5 4 3 2 1 LONG 

 STRUT 



Fig. Dl - Family of ship- 

 like forms 



405 



