Wave Excitationless Ships Forms 



DISCUSSION 



Jerome H. Milgram 



Massachusetts Institute of Technology 



Cambridge, Massachusetts 



During the oral discussion of this paper at the Sixth Symposium on Naval 

 Hydrodynamics, one person mentioned the possibility that wave-excitationless 

 forms might be used for a stable base from which waves could be measured in 

 the open sea. This possibility has been extensively explored with successful 

 results by a number of researchers; see e.g. Kerr (1) or Milgram (2). Both 

 Kerr and Milgram calculated the heaving force on their buoys by neglecting the 

 scattered waves and approximately the force caused by the incident wave alone. 

 A modified form of this calculation is given here. 



Consider a body formed by two cylinders, one of which pierces the free 

 surface (Sketch 1). 



This made from 

 cylinders (1) 

 and (2) 



I 

 (2) 



Sketch 1 



The vertical force on cylinder (1) is called Fj and the vertical force on cyl- 

 inder (2) is called Fj. 



The pressure in an incident sinusoidal wave of amplitude h in deep water is 



P = pghe'^y cos (kx -cot) (1) 



Fj = pghAje' 



kF 



-k2/2 k£/2 

 ; - e 



cos (kx - wt ) 



(2) 



For 



k — << 1 , Fi = -/Oghe" kV cos (kx - cot) , 



(3) 



where v = k^l is the volume of cylinder (1). 



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