The shortcomings of the Froude-Krylov hypothesis have first been overcome 

 in the case of submerged bodies moving uniformly and horizontally close to the cor- 

 rugated free water surface. Later Havelock [41] gave a solution for the spheroid, and 

 Cummins [42] applied his generalized singularity theorem to determine the hydro- 

 dynamic part of the exciting force experienced by bodies of revolution. The distortion 

 of the wave shape is not considered by this approach. The application of Cummins' 

 method to general problems of ship mechanics is promising, although some difficulties 

 still exist in the case of rotational motions [43]. 



The question arises if use can be made of the results found for the rectilinear 

 horizontal motion of submerged bodies, when dealing with surface ships. The problem 

 of heave and pitch has been attacked by Korvin-Kroukovsky. By using an analogy 

 with submerged bodies, he obtained expressions for the exciting force per unit ship 

 length which agree in structure with the corresponding ones for wholly-submerged 



U 



bodies. A dependence of the total force and moment upon the speed ratio — arises. 



c 

 Although this dependence is not supported by Korvin's own experiments, and its exist- 

 ence is denied by Haskind [25], one would feel inclined to assert by analogy that some 

 speed effect should exist. At least one curve published by Haskind appears to support 



0.¥ 



0.2 



-O.t -08 -u * 



heading Into waves 



Figure 2. Coefficients of exciting force and moment in heave and pitch, E~ and Ew,, as functions 



U 

 of U* = — (From Haskind.) 



-M -0.2 -0.2 -0.H- -U* 



fcUowlny wav es heading into Waves 



this conjecture. (See Fig. 2.) Difficulties presented by free surface effects have been 

 discussed by Professor Korvin himself; some of them dealing with the strip method used 

 for computation of damping have been clarified in the meantime by Havelock. It appears 

 that in the most important range of natural periods, the strip method has its definite 

 merits. 



We discuss now the method used by Haskind to determine exciting forces [44] 

 [45] [25]. Haskind's calculation is based on Krylov's work and on the consideration of 

 diffraction effects. In quite an unusual way the ship is pictured by an infinitely long 

 cylinder, whose axis makes the angle X with the wave direction. 



The form of the potential of the free wave suggests a complete potential con- 

 structed as the sum of a part which solves the problem of forced motions in calm 

 water, and a part which solves the diffraction problem. 



Forces due to wave diffraction can be interpreted as due to damping and added 

 mass effects which, however, differ from the common concepts. For side waves the 

 concepts coincide, but denoting the diffraction terms by a superscript (d) one obtains 



#<«"(0) = 0, m< d >(0) = 0, 



iVW(oo) = 0, P)(o) = 0, 

 72 



COS X ?* 0. 



(10) 



