Understanding and Prediction of Ship Motions 



The high coherencies that should actually occur in an adequately resolved 

 properly designed analysis of a vector Gaussian process associated with a long 

 crested random seaway are reflected finally in the papers of the symposium in 

 which the motion of the ship was predicted from the forcing waves. Accurate 

 transfer functions are needed to construct the time domain operators for such 

 predictions. These so-called "predictions" are not strictly predictions in that 

 they use data from the future to a certain extent in order to compute the mo- 

 tions of the ship. A true prediction would be one in which the forcing waves 

 were known only up to a certain time, t = t^ and the motions of the vessel in all 

 degrees of freedom were known up to this same time. The problem would then 

 be to predict the observed value of one of the motions at a time, say, 10 sec- 

 onds into the future, based on just the amount of data available at t = t^. It is 

 evident that this true prediction problem can be solved more accurately for 

 models in long crested waves. From a discussion in this section and from the 

 results on short crested waves it should prove to be more difficult to predict 

 the motions of an actual ship in actual waves 10 seconds into the future. Never- 

 theless, the ability to do this is still needed, and an adequate investigation of 

 this problem needs to be made. The past history of the motions of the vessel 

 and the past history of the waves as observed at some point near the vessel can 

 be combined to provide a prediction of the motion of the vessel at some future 

 time. 



THE SOLUTION OF SPECIFIC PROBLEMS 

 THAT ARE NOT LINEAR 



From different assumptions, a large number of linear models to describe 

 ships in waves have been developed. The more advanced models may even be 

 nonlinear in the beam parameter and still linear in the forcing wave systems. 

 Nevertheless, roll and certain extreme motions will eventually have to be 

 treated by nonlinear equations. 



A number of realistic problems have been formulated in wave theory and in 

 ship motion theory that are not linear. These problems have been solved. The 

 assumption of linearity by St. Denis and Pierson and by Pierson (1957) is no 

 longer a restriction due to the lack of techniques for solving problems that are 

 not linear. 



An interesting example of a procedure that does not get too deeply involved 

 in the intransigent aspects of the subject is the analysis of the forces due to 

 waves on a vertical piling as given by Pierson (1963) and by Pierson and 

 Holmes (1965). 



Consider a pile in water with long crested waves passing it. The velocity 

 field due to the waves in the water will exert a force on a small segment of the 

 pile given by Eq. (31). 



f(t) = kjU(t)|U(t)| + k^UCt) . (31) 



Given the depth of the water, the spectrum of the waves, and the depth of the 

 pile segment at which the force is measured, the spectra of U(t) and U(t) can 



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