Application of Wavemaking Resistance Theory 



2. The viscosity effect is negligible and the potential theory can be used in 

 the study of ship-created waves. 



The first assumption is usually satisfied by selecting a beam that is very 

 small in comparison uith the length and the draft. Such ships are called thin 

 ships. Since a thin ship has no practical value, the theory has also been applied 

 to ships with practical beams in the hope that some good may result despite the 

 limitations of the theory. 



Fortunately, while a small beam is a sufficient condition for a small free- 

 surface disturbance, it is not a necessary one. If a practical (thick) ship can be 

 designed which disturbs the free surface as little as a thin ship, the linearization 

 of the free-siirface condition should be applicable to this practical ship as well. 

 Since the main portion of the free-surface disturbance is due to the free waves 

 which cause the wavemaking resistance, the theory should be applicable to thick 

 ships of low wave drag as well as to thin ships. Therefore, the pertinent ques- 

 tion to be asked with regard to the linearization of the free-surface condition is 

 whether or not the wavemaking resistance is small rather than whether or not 

 the beam is small. If we limit our study only to hull forms with very small 

 wavemaking resistance, the theory is valid so far as the assumption about the 

 free surface is concerned. 



In later sections, a procedure will be given for obtaining low wave-drag 

 ships under the restraint of practical design conditions. Let us first examine 

 more carefully the argument for using the theory to design low wave-drag prac- 

 tical ships. For this purpose, the comparisons made in the past betv,'een theo- 

 retical and experimental results have been carefully re-examined. Unfortimately, 

 most of these comparisons have severe defects except those of Inui. He has 

 clearly shown that the linearized condition on the ship surface is not accurate 

 enough to obtain the singularity distribution of a given hull geometry for thick 

 ships, or vice versa. If this situation is not improved, the theoretical model 

 (singularity distribution) and the experimental model are not equivalent. Inui 

 has been criticized by many people for employing a higher than first-order ap- 

 proximation on the ship surface while keeping the first-order approximation on 

 the free-surface condition. His approach has been fully justified by the impor- 

 tant results he has so obtained. 



Since at this point we are examining only the consequence of the linearized 



free- surface condition, our study is confined to the comparison in the Froude 

 number range where the viscosity effect is relatively small. In many cases, 

 due to the fact that the theoretical and experimental models are not equivalent, 

 such comparisons are rather confusing. Generally speaking, the percentage 

 differences betw-een theoretical and experimental results are smaller when the 

 level of wavemaking resistance is lower. Emerson's paper [l], based on Wig- 

 ley's experimental work, definitely shows this tendency. Fortunately, we have 

 the comparisons of the S-series models made by Inui [2]. In each of these cases, 

 the theoretical model and the experimental model are equivalent. Table 1 gives 

 the theoretical and the experimental wavemaking resistance coefficients and the 

 corresponding Froude numbers taken from Inui's published curves. Some geo- 

 metrical parameters of these models are also listed. Figure 1 shows a simple 

 comparison of the theoretical and experimental wavemaking resistance 



nil 



