Understanding and Prediction of Ship Motions 



The first of these papers was presented at the Wageningen meeting by Kato, 

 Motora, and Ishikawa (1957). They restrained their model to remain in a beam 

 seas attitude, with natural confused waves. The model had zero forward speed. 

 Its roll amplification factor, It^C-:^) I , was determined in tank tests with regular 

 waves, and this operator was used with the measured wave height energy spec- 

 tra to predict roll response energy spectra in random waves. The calculations 

 were then compared with measured energy spectra for roll, with good agree- 

 ment being found. The wave and roll amplitudes were rather small, and so the 

 results were not conclusive. Also, the paper lacked certain model details, and 

 so one does not know, for example, whether the model had bilge keels. Never- 

 theless, these experiments were among the first to be conducted for checking 

 the superposition hypothesis, and the authors' general conclusions have since 

 been corroborated. 



Earlier this year, Lalangas (1964) published a report on some Davidson 

 Laboratory experiments directed toward the same goal. A Series 60, Cg = 0.60, 

 model (with bilge keels) was used, and the statistical design of the experiments 

 was quite similar to Dalzell's. Only beam seas were studied, but forward speed 

 was included, up to a Froude number of 0.156. Essentially the result was the 

 same as in the tests of Kato, et al., viz., superposition does work for roll re- 

 sponses. The irregular waves in Lalangas's tests varied in severity up to a 

 low state 7. 



In a certain sense, we are back where we were eleven years ago, that is, we 

 now turn our attention again to the behavior of ships in sinusoidal waves. There 

 is, of course, one major change: We now know that the study of such idealized 

 environments has a real relevance to the physical problem which occurs in na- 

 ture. Moreover, regular wave problems have not been ignored during this dec- 

 ade. There has been much progress, although unfortunately it will not be possi- 

 ble to make such definitive statements in this area as in the area of random sea 

 phenomena. 



THE EQUATIONS OF MOTION 



Equations in the Frequency Domain 



A ship in a seaway can be completely characterized (for studies of its mo- 

 tions) by a set of six frequency response functions depending on ship speed, wave 

 encounter, and angle of wave encounter. If these f.r. functions are known, the 

 ship can be treated as a "black box." An input wave system is selected which is 

 a sum (or integral) of many sinusoidal waves, and the output is calculated by 

 multiplying each input wave amplitude by the appropriate value of the f.r. func- 

 tions and adding all of the responses. The experiments cited in Chapter II have 

 demonstrated the validity of these statements at least with respect to heave and 

 pitch motions in head seas and roll motions in beam seas. We may perhaps ex- 

 pect difficulties in following seas (see Grim (1951)) and also with the other 

 modes of motion. In the case of following seas, it is well-known that non- 

 linearities are important, and for yaw and sway we simply do not have much 

 data. We shall proceed on the premise that the same laws of linearity apply in 

 these other conditions, but it must be recognized that our conclusions may be 

 valid only for those modes which have been extensively studied experimentally. 



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