Understanding and Prediction of Ship Motions 



symposium. These comments apply in particular to the papers by Dr. Ogilvie, 

 Dr. Ochi, and Drs. Breslin, Savitsky, and Tsakonas. 



The papers by Fuchs and MacCamy (1953) and by St. Denis and Pierson 

 (1953) have been cited as initiating the study of the motions of ships in real 

 waves, the first from the time domain viewpoint and the second from a spectral 

 viewpoint. The first is often thought of as deterministic and as having little to 

 do with the Gaussian properties of real waves. The second is thought of as 

 highly dependent on the assumption of Gaussian behavior for the waves and on 

 the principle of linear superposition. 



The first is nevertheless highly dependent on many of the same assump- 

 tions of St. Denis and Pierson. Since waves are very nearly Gaussian, it is 

 useful to get the spectra and cross spectra that describe the response of a ship 

 to long crested waves in order to obtain an accurate time domain operator for 

 the application of the procedures of Fuchs and MacCamy. Their model is just 

 as linear and just as dependent on a linear hypothesis as that of St. Denis and 

 Pierson. 



In actuality the work of Fuchs and MacCamy is much more restrictive than 

 the work of St. Denis and Pierson, and much of the work described at this sym- 

 posium is too restrictive for direct application to real ships in real waves. The 

 work of Fuchs and MacCamy is strictly applicable only to ships in long crested 

 waves. Long crested waves are an abstraction not met in nature. The work of 

 St. Denis and Pierson, and its completion so as to include co- and qviadrature 

 spectra, by Pierson (1957) is applicable to actual ships in actual waves and pro- 

 vides valuable guidance in the study of ships and other floating objects in real 

 waves. Studies such as those of Canham, Cartwright, Goodrich, and Hogben 

 (1962) and O'Brien and Muga (1965) show the value of spectral and cross -spectral 

 analysis. More can be done in a full utilization of these results, however. 



The concept of linearity invoked by St. Denis and Pierson is not as essential 

 to their theory as it seemed at the time although even for such extreme condi- 

 tions as slamming, the theory yields useful results as in the work of Tick (1958) 

 and in the paper of this symposium by Dr. Ochi. Recent work has extended the 

 linear model of the seaway to a number of nonlinear models, and for specific 

 problems nonlinear models concerning waves and the effect of waves on ships 

 and some other objects have been developed. 



SfflPS IN A SHORT CRESTED SEAWAY 



If T7(x, y, t) is the sea surface, and if S(aj, 6) is the variance spectrum of the 

 waves, one can write that 



7](x,y, t) = cos (-^^(xcos^ + ysin^) - cot ^ e(a;, 0)J ^25(0^, (9) dojdO . (1) 



Consider a point moving in the negative x direction with the velocity, v. 

 The coordinates of this point are given by Eq. (2) as x^.y^. 



221-249 O - 66 - 7 



81 



