Application of Wavemaking Resistance Theory 



4. Pien, P. C. and Moore, W. L., "Theoretical and Experimental Study of 

 Wavemaking Resistance of Ships," Internation Seminar on Theoretical Wave 

 Resistance, University of Michigan, Ann Arbor, Michigan (August 1963) 



5. Wu, J., "The Separation of Viscous from Wavemaking Drag of Ship Forms," 

 Journal of Ship Research, Vol. 6, No. 1 (June 1962) 



DISCUSSION 



G. P. Weinblum 



Institutfur Schiffbau 



University of Hamburg 



Hamburg, Germ,any 



Leaving aside basic theoretical considerations in the field of wave resist- 

 ance, we consider Dr. Pien's recent proposal a valuable contribution following 

 which bodies are generated in a uniform flow by distributing singularities over 

 a suitably chosen skeleton surface instead of over the central plane. By these 

 "Pienoids" a serious difficulty has been mitigated when investigating hull forms 

 of least or low wave resistance; the recent trend to study flow conditions by de- 

 termining singularities over a prescribed body surface makes an optimisation 

 of the latter obviously impossible. 



In the present paper an attempt has been made to apply theory to the solu- 

 tion of a rather general engineering problem, the determination of hull forms of 

 low total resistance (instead of low wave resistance, etc.). The exposition of 

 this important task is in my opinion slightly impaired by some global and dep- 

 recating statements made by the author. Some aspects of the problem have 

 been clearly described by D. W. Taylor in his "Speed and Power of Ships"; cf., 

 his famous sketch representing the total rest and frictional resistance R^, R^. 

 and Rf of a given dimensionless form and V - const, as function of the length. 

 The essential difficulty consists in finding the wave and viscous drag components 

 leading to an optimum. 



It is typical and unavoidable that one has to face the viscous resistance 

 problem when dealing with the wave resistance. The author asserts that we 

 know how to shape a deeply submerged body of low viscous drag. This is cor- 

 rect as long only as a qualitative reasoning is concerned. Reference is made to 

 the pertaining formulas 



C, = (1 + n)C,o 



with 



n = 2.2 B/L + ... 

 1137 



