Wave Analysis Techniques to Achieve Bow-Wave Reduction 



draft. It may be noted in passing that the empirical bulb design actually tested — 

 being represented by the coordinates (0,1) in the diagram — is a near hit to the 

 theoretical optimum for the ballast condition, and this was to the author's knowl- 

 edge also the aim of the designer in the present case. However, there is still 

 some room for minor overall improvement, and this diagram serves to illus- 

 trate the type of practical recommendations that can be made to the designer 

 with the aid of the wave analysis techniques in this paper. 



ACKNOWLEDGMENTS 



This work has been performed in the Hamburgische Schiffbau-Versuchs- 

 anstalt (HSVA) at the instigation of the Director, Professor Dr.-Ing. Hermann 

 Lerbs, and with the financial support of the Deutsche Forschungsgemeinschaft. 



The wave profile measurements on the mathematical model Inuid S-201 re- 

 ported in Part I of the paper were conducted in collaboration with Professor 

 Lawrence W. Ward of the Webb Institute of Naval Architecture and Dr. Klaus 

 Eggers of the Institut fur Schiffbau der Universitat Hamburg as part of a related 

 research program aimed at comparing different methods of wave analysis. A 

 complete report on this work is currently in preparation. 



The wave records of the cargo ship model with and without a bulb, presented 

 in Part II, were obtained during routine testing for a German shipyard, 

 Orenstein-Koppel und Lubecker Maschinenbau Aktiengesellschaft, to whom the 

 author is greatly indebted for kind permission to conduct these measurements 

 and to publish most of the information. 



The author is also grateful to Mr. Harald Keil of the Institut fur Schiffbau 

 for his assistance in automatic data acquisition and to Mr. Walter Alef of the 

 HSVA for his help in data reduction and computer programming. 



NOMENCLATURE 



(Unless otherwise specified, all lengths have been rendered nondimensional 

 by multiplication with the fundamental wavenumber k^ and all wavenumbers 

 have been rendered nondimensional by division with k^.) 



A Dimensional amplitude of an elementary wave in a tank of 

 width 



A = kgA Nondimensional wave amplitude 



b Tank width 



c,s Fourier transforms of Ux), see Eq. (12) 



Cy,Sy Analogous Fourier transforms of ^y(x) 



C*,S* Weighted Fourier transforms, see Eq. (17) 



Cp, Sp Fresnel integrals, see Eq. (22) 



763 



