Sharma 



In theory, this matching can be accomplished by purely analytical means. 

 Using the well-known concept of Havelock sources and representing the main- 

 hull/bulb combination by distributed and concentrated singularities respectively, 

 one can derive systems of extremely low, or even zero, theoretical wave resist- 

 ance. Perhaps the most striking of such results have been obtained by Yim, 

 whose paper (1) to the last ONR Symposium on Naval Hydrodynamics at Bergen, 

 Norway, in 1964 may be consulted also for references to previous literature on 

 the subject. However, the underlying linearized theory is known to be quite in- 

 adequate for practical purposes. It generally fails to predict with sufficient ac- 

 curacy the actual wave-making characteristics of even simple ship forms. 



Therefore, for the present work a semiempirical approach as advocated by 

 Inui, for example in his 1962 paper (2), was adopted. In this method theory is 

 only used to estimate the bulb wave system, while the wave-making character- 

 istics of the main hull are determined essentially from model experiments. As 

 rightly emphasized by Inui the concept of a free wave spectrum is extremely 

 useful in matching the bulb wave pattern to that of the main hull, for this enables 

 one to adjust the two systems by considering the individual amplitudes and 

 phases of component plane waves rather than the complicated geometry of the 

 integrated two-dimensional wave pattern. In actual application, however, Inui 

 and his collaborators seem to have used the general configuration of the meas- 

 ured wave crests and troughs to define a fictitious point of origin ahead of the 

 bow and have then taken radial wave profiles through this point for further eval- 

 uation, cf. Takahei (3). This method requires laborious stereophotogrammetric 

 measurements of the entire wave system and, in effect, fails to take full advan- 

 tage of the simple and elegant concept of the free wave spectrum. 



For the present investigation it was decided to make a consistent use of the 

 elementary wave concept by first analyzing the measured wave system of the 

 main hull to obtain the spectrum and then adjusting the bulb to it. The basic 

 step, therefore, was to find a convenient and practical method of obtaining the 

 empirical spectrum from wave measurements capable of being taken, if possi- 

 ble, during a routine resistance test. Extensive testing previously conducted by 

 the author (4-6) on a mathematical model, designated as the Inuid S-201, had 

 established the validity of a transverse-cut method of deriving the free wave 

 spectrum from Fourier transforms of two or more wave profiles measured 

 along straight lines normal to the direction of motion of the model. However, 

 this method appeared to be somewhat inconvenient for the present purpose, 

 since transverse cuts can be measured only by moving wave probes across the 

 towing carriage during the model run, unless the even more difficult stereo- 

 photogrammetric technique is used. Moreover, there is no unique way of break- 

 ing up the waves measured behind the model into contributions from the bow and 

 the stern which may be desirable from the point of view of bulb design. 



Hence it was decided to try out the two longitudinal-cut methods of wave 

 analysis originally suggested by the author in 1963, see Ref. 4a. These require 

 only the knowledge of wave height or transverse wave slope along a single 

 straight track parallel to the direction of motion of the model. This information 

 can be obtained rather easily by locating a stationary wave probe at some suit- 

 able point in the towing tank and taking time -dependent records while the model 

 passes by, without any interference with the routine testing. Incidentally, this 



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