Added Resistance of Ships in Waves 



and 



at S. 4>d is the diffraction potential due to the incident wave c^q, and 0^ is the 

 radiation potential due to the oscillatory motion of the body for the case of am- 

 plitude unity. 



These functions can be determined by solving the boundary value problems. 

 We shall restrict ourselves to slender bodies and to frequencies for which k is 

 of order unity. It is well known that these restrictions lead to the results of the 

 two-dimensional strip theory (5). 



The mean force and moment acting horizontally on the ship can be related 

 to the rate of change of linear momentum within the fluid domain bounded by the 

 ship's hull, the free surface, and a control surface at infinity. The result is de- 

 rived by Maruo (3) and Newman (4) and reads for the two force components 



F^ = -j ^— = ^ (cos + cos /3) |H(0)|^de , (1) 



Jo 



-^/ogh^B^L 16776 2 



and 



F =-^ ^ =-r-A (sin e + sin yS) |H(e)i'd^, (2) 



4 

 where H(0) is the Kochin function 



•'-1 ''c ( X ) 



These expressions are still valid for bodies of arbitrary shape. 



We shall apply this result to a slender ship for the case of k being of order 

 unity. 



The first order term in the series expansion of Eq. (1) and Eq. (2) with re- 

 spect to e will be derived in the next section. 



ASYMPTOTIC EXPANSION 



The expression for H(0) can be written as 



639 



