Salve sen 

 CONCLUSIONS 



This work clearly proves the importance of the effect of nonlinearity at the 

 free surface, and it shows how much better results can be achieved by the 

 second-order theory than by the linear theory. The speed range and submer- 

 gences are also indicated for which linear and for which second-order theory 

 may be applied. 



The following conclusions can be drawn for free-surface flow past sub- 

 merged two-dimensional foil-shaped bodies: 



1. The second-order theory gives very good results at moderate speeds 

 (u/Vgb < 0.72) and submergences larger than 3-1/2 times the thickness of the 

 body. 



2. At very low speeds the second-order theory predicts wave heights sev- 

 eral times the size given by the linear theory. The agreement between experi- 

 ment and second-order theory is surprisingly good at these very low speeds. 



3. For checking the accuracy of the theory a comparison between theoreti- 

 cal and measured wave profiles should be used rather than a comparison of wave 

 resistance data. 



4. Due to the wave breaking phenomenon at smaller submergences, the 

 perturbation theory should not be used over the entire speed range if the sub- 

 mergence is smaller than three times the thickness of the body. The experi- 

 ments show that at a submergence three times the thickness of the body the 

 waves break in the speed range 0.45 < UA^ < 0.90; and at smaller submer- 

 gences the waves break in an even larger speed range. 



5. Both the linear and the proposed second-order theory give rather poor 

 results at higher speeds (u/Vib > 0.72). This is believed to be due to the inac- 

 curate mathematical representation of the body at these speeds. 



We should be careful in extending any of these conclusions to the three- 

 dimensional ship problem. It seems reasonable to conclude however, that non- 

 linear free -surface effects are most likely more important for surface ships 

 than previously believed. 



Further research should be carried out in this area. Presently the author 

 is applying a consistent second-order theory which seems to predict the wave 

 resistance and the wave profiles very well also at higher speeds. In addition to 

 this work the two following problems deserve attention: 



1. A thorough investigation should be made of the viscous effects on free- 

 surface flow past a cylinder by means of wake study and possibly also by apply- 

 ing boundary -layer suction control. 



2. Work should be extended to include three-dimensional submerged bodies. 



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