Pien 



doublet, the first restraint is related to the VCB and the second one is related to 

 the volume of a bulb. In any specific design problem, we can choose any number 

 of the ten elements and impose any number of the three available restraints on 

 each of the chosen elements. 



The computing program performs basically one operation. The free-wave 

 amplitude is computed from all the elements specified in the input data. Then a 

 chosen element which is not specified in the input is determined under the spec- 

 ified restraints so that the resultant free-wave amplitudes of this particular 

 element and that specified in the input will yield a minimum wavemaking resist- 

 ance at the design Froude number. If no element is specified other than those 

 in the input, the program simply computes the wavemaking resistance and the 

 free-wave amplitudes of the singularity distribution given in the input at the 

 specified Froude number range and interval. 



To obtain a singularity distribution with a low level of wavemaking resist- 

 ance, only two or three elements are required for a main hull form. The re- 

 maining surface singularity distribution elements are provided mainly for the 

 purpose of meeting the hull geometrical requirements. 



The computing program is very flexible. We can start either with the de- 

 sign of main hull form alone and later consider the size and shape of the bulb, 

 or we may first specify a bulb and then design a main hull form in conjunction 

 with this bulb. 



A number of interesting theoretical analyses have been performed by using 

 the computer program. The results are given in later sections. 



Hull Form Tracing From a Given Singularity Distribution 



A second computer program has been developed which can be used to develop 

 a set of hull lines from a given singularity distribution. This program is an im- 

 portant link between a theoretical model and its corresponding experimental 

 model. The basic assumption made here is that the free surface can be replaced 

 by a rigid plane. Inui has shown in Ref. 2 that in the low Froude number range, 

 the error resulting from this assumption is not serious so far as developing 

 hull lines is concerned. Therefore, at the same Froude number, the less the 

 wavemaking resistance, the closer the free surface will approach the rigid plane 

 assumption. That means if we limit ourselves only to hull forms of low wave- 

 making resistance, the error involved in the rigid plane assumption will be even 

 less serious. 



The input data for this program specify all the singularity distribution ele- 

 ments involved in the theoretical representation of the hull form under consid- 

 eration. The first item the program computes is the additional bottom surface 

 singularity distribution required for obtaining flat keel line or flat bottom. The 

 program will trace a specified number of streamlines generated by all the sin- 

 gularity distributions involved. The output of this program consists of a table 

 of offsets which define a hull geometry. The details of this computation are 

 given in Refs. 2 and 4, 



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