Sharma 



height at a suitable fixed point in the towing tank while the model passes by at a 

 steady speed, during a routine resistance test for example. A simple Fourier 

 transform analysis of this record based on linearized potential theory then 

 yields the free wave spectrum and the wave resistance of the model. The 

 method has been numerically checked on different theoretical wave systems of 

 predetermined spectra and experimentally verified on the mathematical model 

 Inuid S-201. All essential numerical and experimental data leading to this con- 

 clusion have been reproduced in the paper, and others working in the field are 

 invited to check the author's or their own methods on it. 



One of the possible practical applications of this new experimental tool in 

 ship-model testing would be to use the empirical free-wave spectrum of a main 

 hull determined in this way as a basis for the design of an optimum additive bulb 

 adapted to minimize free surface deformation, reduce resistance, and improve 

 performance. (Such an application is described in Part II.) 



Another possible application would be to analyze geosim model and full-size 

 ship wave patterns by this method with a view to investigate scale effects and 

 improve ship model correlation. It is hoped that those with the appropriate fa- 

 cilities at their disposal will take up the problem. 



PART II - SUPPLEMENT TO PART I 



The numerical and experimental verification of a longitudinal-cut method of 

 analyzing the measured wave system of a ship model with a view to determine 

 its free wave spectrum was reported in Part I. The purpose of the following 

 addendum is to round out this report by including a concrete example of possible 

 practical application of this method to the problem of optimum bow design. 



The basic empirical information needed for this work consisted of longitu- 

 dinal wave profiles, measured during routine resistance tests at the HSVA, of 

 two alternative designs (one with and the other without a bulbous bow) of a cargo 

 ship model. Both the main hull and the bow bulb were of purely empirical de- 

 sign. The relevant parameters of the models tested are reproduced in Table 9. 

 It may be noted that two operating conditions were specified; hence four sets of 

 resistance and wave measurements were taken. The data analyzed and reported 

 in the following were obtained at model speeds corresponding to the designed 

 service speeds of the full-size ship in the fully loaded and ballast conditions. 

 The transverse location and longitudinal extent of the profiles recorded and 

 evaluated was very similar to that shown in Fig. 4. 



An analysis of the wave height records by the method described in Part I 

 yielded directly the free wave spectrum of the model with and without a bulb. 

 From this the differential bulb spectrum was derived by taking the vector differ- 

 ence between the wave amplitudes with a bulb and those without a bulb at the 

 same speed assuming the principle of linear superposition of the wave patterns 

 created by the main hull and the bow bulb. The three sets of amplitudes obtained 

 in this way are shown as functions of the transverse wavenumber u in Fig. 9 for 

 the fully loaded condition and in Fig. 10 for the ballast condition. It will be 

 noted that the amplitude spectrum of the model (both with and without a bulb) 



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