Breslin, Savitsky, and Tsakonas 



motion and presented methods for determining the probabilistic behavior of a 

 ship in a random sea. A second method of analysis, which is complementary to 

 that of St. Denis and Pierson, was introduced by Fuchs and MacCamy [2], This 

 later method is not statistical, but deterministic; it is based, therefore, not on 

 the knowledge of the statistical properties of the sea, but on that of the actual 

 time history record of the sea surface. 



The statistical approach makes use of spectral analysis techniques and the 

 characteristics of the ship response to random wave excitation are defined in 

 terms of an energy spectrum based on frequency of wave encounter. This is the 

 so-called transfer function method whose application has been successfully dem- 

 onstrated by many researchers over the past years for a variety of marine 

 craft, i.e., St. Denis and Pierson [1] and Dalzell [3] in the case of motion of dis- 

 placement ships; Dalzell [4] for the case of ship bending moment; Savitsky [5] 

 for submerged bodies in irregular waves; and Bernicker [6,7] for the case of 

 fully wetted and super- ventilated surface piercing hydrofoil systems. 



The deterministic approach employs the concept of the impulsive response 

 function, as given in linear analysis, to define the time history of ship motion in 

 terms of the actual time history of the surface wave profile of the irregular sea. 

 As the name implies, the impulsive response function describes the time history 

 of the response of a given system when acted upon by an input consisting of a 

 unit impulse at zero time. Superposition of these unit impulses to represent the 

 actual wave excitation yields the total response of the system. Fuchs and Mac- 

 Camy [2,8] first applied this technique for simple bodies in a random head sea. 

 In recent years, the Davidson Laboratory, Stevens Institute of Technology, has 

 investigated the application of this deterministic technique to predicting the 

 random motions of a variety of marine vehicles, including displacement ships, 

 hydrofoil craft, and submerged bodies in irregular waves. It is the purpose of 

 this paper to present a review of the deterministic technique, to discuss its 

 limitations, and to compare the results of the analytical studies conducted at 

 Davidson Laboratory with experimental data. Some of these results have al- 

 ready appeared in the published Davidson Laboratory reports, but will be sum- 

 marized herein in an attempt to form a unified presentation. 



This work was sponsored by several bureaus of the U.S. Navy, including the 

 Bureau of Ships, Bureau of Naval Weapons, and Office of Naval Research. The 

 preparation of this paper was sponsored by the Davidson Laboratory, Stevens 

 Institute of Technology. 



THEORETICAL FOUNDATIONS 



The linear theory of the motions of bodies in waves has been the subject of 

 many papers and presentations in the past. As a result, there are several clear 

 analyses of bodies in both regular and irregular waves, the latter case having 

 been dealt with by spectral procedures. However, the deterministic or instan- 

 taneous response of bodies in a given, nonuniform, temporally varying wave has 

 not been given an entirely clear analysis beginning with the equations of motion. 

 The procedures used thus far have treated the motion as the output of a linear 

 system due to a wave input. This involves the identification of (for systems with 



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