Lin, Paulling, and Wehausen 



this preference: the theorem of Weyerstrass from a mathematical point of view 

 and the attempt of using the wisdom of art embodied by "spline curves." The 

 "ugly" wiggled forms obtained by the authors justify my dislike of trigonometrical 

 series as long as a relatively small number of terms is admitted. Exact solu- 

 tions (Karp, Maruo, Kotik, etc.) indicate that the wiggles are not significant re- 

 sults but an outcome of the use of the functions mentioned. In the meanwhile it 

 follows from a kind information by Prof. Wehausen that the wiggles are smoothed 

 out when a larger number of terms dependent upon x is used. 



Notwithstanding the offense against beauty committed by the authors the 

 theoretical investigation has furnished valuable information on the 



(a) low magnitude of resistance up to relatively high F when a large num- 

 ber of terms is used, 



(b) influence of vertical displacement distribution on resistance, and 



(c) dependence of resistance upon number of form parameters. 



In agreement with my experience when testing forms of extremely low wave 

 resistance (by calculation) the authors are disappointed by their experimental 

 results. The high resistance measured may be due (a) principally to the fact 

 that viscosity destroys the calculated favorable interference effects. This ap- 

 plies even to fine streamlined forms in the afterbody (compare our tests with a 

 model Cp = = 0.52, communicated at Ann Arbor Proceedings 1963, (b) to sep- 

 aration and excessive viscous form drag due to the stern bulb. The author's 

 decision to test a more normal form is commended, further, forms with bow 

 bulb alone could be tested. But in the light of our earlier experiments (Schiffbau 

 (1936) point (a) may be more decisive than (b)), (c) the authors point out at the 

 possibility that second order terms in the resistance integral may become im- 

 portant when developing optimum forms based on first order theory. This is a 

 new idea which may be checked by evaluating a second approximation using 

 Sisov's formula. Such work is going on under the guidance of Dr. Eggers at the 

 Institut fur Schiffbau, University Hamburg. 



REPLY TO THE DISCUSSION 



Wen- Chin Lin, J. Randolph Paulling 

 and J. V. Wehausen 

 University of California 

 Berkeley, California 



First of all we should like to state that we are pleased that Dr. Pien has found 

 it quite clear how our results were obtained, even though their significance may 

 remain cloudy. It seemed particularly important for these tests that this should 



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