acting on a floating body. It was first pointed out by Haskind 

 (1948, 1959) that the mean drift force could be formulated 

 through application of the integral momentum equation together 

 with a knowledge of first-order potentials. Muro (1960) also 

 independently gave a general treatment of the mean drift-force 

 and Newman (1967) extended Muro's results to include the moment 

 and, in addition, introduced the slender body approximation into 

 the analysis. Faltinsen and Michelsen (1974) applied Newman's 

 formulas to evaluate the mean drift-force using the three-dimen- 

 sional distributed source procedure. In Newman's notation the 

 formulas for the force components in the horizontal plane and mo- 

 ment about a vertical axis are given by 





(2a) 



/^ = _^r //Yc&j/^($-*f/s> - smb) c/e (2b) 



(2c) 



where H(&> is the Kochin function. Without giving further form- 

 ulas, it may be noted that the Kochin function requires a know- 

 ledge of the first-order potentials associated with diffraction 

 of the incident wave as well as the radiation potentials for all 

 six degrees of freedom. Thus, the drift-force calculation re- 

 quires a knowledge of the first-order motions. 



A second method for calculation of the drift is based on a 

 straightforward integration of the pressure over the wetted sur- 

 face of the vessel. This procedure was first presented by 

 Garrison (1974) for three-dimensional floating bodies although a 

 term was left out of the final expression which accounted for the 

 the effect of the displacement of the body. Pinkster and van Oor- 

 rtmerssen (1977) later gave the correct form of the expression 

 for the drift-forces and moments. The force, for instance, is 

 given by 



J. 



(3) 



ye 



in which Uy- denotes the total first-order potential, ^o" ,Yt,' 

 and J^y* denote the complex amplitude of the three comp- 

 ponents of displacement of a point on the hull, A^''-* denotes 

 the first-order correction to the unit normal vector on the mean 

 position of the hull denoted by Ho . In (3) the first three in- 

 tegrals are carried out over the wetted surface of the hull below 



51 



