Application of Wavemaking Resistance Theory 



If the hull geometry so obtained is not satisfactory, we may either introduce 

 additional singularity distribution elements with the necessary restraints or 

 modify the restraints on the original singularity distribution elements. Based 

 on the gross effects of either modifying the restraints of a particular element 

 or introducing a new element to the singularity distribution, we may decide what 

 modifications should be made on the restraints or which additional elements 

 should be introduced and then make corresponding changes in the input data for 

 the first computer program. The output will give a new singularity distribution 

 optimized with new elements or with new restraints. The iteration between 

 these two programs is necessary in order to obtain a good compromise between 

 hull resistance and hull geometry. 



NUMERICAL EXAMPLES IN WAVEMAKING RESISTANCE 



In the previous sections two computing programs have been described. The 

 first one is used to obtain an optimum singularity distribution for a ship design 

 problem or to compute wavemaking resistance curve and free-wave amplitudes 

 of a given singularity over a specified range of Froude numbers. The second 

 program is used to compute the hull geometry generated by a given singularity 

 distribution. This section gives a few numerical results obtained from these 

 programs. 



The first example is intended to show that a thick ship can produce less 

 free- surface disturbance and wavemaking resistance than a thin ship. The ques- 

 tion of whether a ship is thin or not is a relative matter, and so is not easy to 

 define. It may be thin enough at high Froude numbers and yet not be considered 

 thin at low Froude numbers. Model S-101 of Ref. 2 is arbitrarily considered to 

 be thin for Froude numbers greater than 0.30, based on the fact that the theo- 

 retical and experimental wavemaking resistance values are then in reasonably 

 good agreement, as shown by the comparison of the computed and measured c^ 

 curves in Fig. 2. This model is generated by a surface source distribution on 

 a central plane having the following density expression: 



M(^,0 = 0-4^ 



(9) 



with - 1 < ^ < 1 , 

 ratio is 13.37. 



and - 0. 10 < ^ < 0. The body plan is shown in Fig. 4. The L/B 



We can now show that a model can be found with much smaller L/B ratio 

 and much greater displacement-length ratio, but with less wavemaking resistance 



Fig. 2 - The computed and nneasured 

 C curves of Model S-101 



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