Ogilvie 



yield any results that were not obtained previously by simpler means. 

 However, it is instructive to consider this problem by this method 

 because the results are rather obvious and it is then clear how the 

 formalism is used in place of some common physical arguments. Then, 

 in the more complicated forward-speed problem, in which physical 

 insight is less reliable, the same formalism can be applied with 

 reasonable faith in its predictions. 



Only the slender -body idealization of a ship has led to useful 

 prediction methods in the ship-motion problem.* The thin-ship 

 model, which was intensively studied from the late 1940^s until the 

 early 1960's, was useful for certain restricted aspects of the prob- 

 lem. For example, the damping of heave and pitch motions, as 

 predicted by thin- ship theory, is fairly accurate. But the complete 

 theory is deficient, A straightforward one-parameter analysis 

 leads to the prediction of resonances in heave and pitch with no 

 added-miass or damping effects, as shown by Peters and Stoker 

 [ 1954] , (See also Peters and Stoker [ 1957] and Stoker [ 1957] .) 

 A multi-parameter thin- ship analysis is apparently satisfactory in 

 principle, as demionstrated by Newman [ 1961] , but no one has used 

 it for prediction purposes. It is too complicated. 



Slender-body theory at one time appeared to have comparable 

 difficulties, but these have been largely removed in recent years, 

 and a theory which is essentially rational now exists and is fairly 

 successful in predicting ship motions. 



In early versions of the slender-body theory of ship motions, 

 all inertial effects (both ship and fluid) were lost in the lowest-order 

 approximation, along with hydrodynamic damping effects. The theory 

 was even more primitive than the classical Froude-Krylov approach. 

 Excitation was computed from the pressure field of the waves, un- 

 disturbed by the presence or motions of the ship, and the restoring 

 forces were simply the quasi- static changes in buoyancy and moment 

 of buoyancy. Even the mass of the ship was supposed to be negligible 

 in the lowest-order theory. 



These deficiencies are removed by assuming that the fre- 

 quency of motion is high, in an asymptotic sense. That is, if one 

 assumes that the frequency of sinusoidal oscillation is 0(e' ) , 

 then the ship inertia force is the same order of magnitude as the 

 excitation and the buoyancy restoring forces. The hydrodynamic 

 force and moment also enter into the calctilation of ship miotions at 

 the lowest order of magnitude. This was all recognized, for example, 

 by Newman and Tuck [1964] , However, correcting the slender-body 



Note that "strip theory" is a special case of "slender-body theory," 

 € is the usual slenderness paranaeter. 



746 



