Understanding and Prediction of Ship Motions 



Finally, he conducted a few tests with the Cg = 0.70 model in irregular 

 waves and obtained the f.r. functions in exactly the way Dalzell did. 



Figure 5 is drawn from data in Gerritsma's paper and shows pitch and 

 heave f.r. functions for the Series 60 model (Cg = 0.70) at F = 0.20. Heave am- 

 plitude, z^, has been divided by wave amplitude, r, and pitch amplitude, <p^, 

 has been divided by the maximum wave slope of the sinusoidal wave, a^. 6* is 

 the relative phase between heave and pitch (positive for heave lagging pitch). 

 Five curves appear in each section of Fig. 5: 



1. Response measured in regular waves. 



2. Response calculated from the equations of motion, with coefficients de- 

 termined experimentally and forcing functions determined from tests of re- 

 strained models in regular waves. 



3. Response calculated as in (2), but with all coupling coefficients arbi- 

 trarily set equal to zero. 



4. Response from wave and motions spectra. 



5. Response from wave and motions cross-spectra. 



(Of course, (4) does not apply to the figure for phases, since no information on 

 phase is obtainable from ordinary power spectra.) It is seen that the f.r. fxinc- 

 tions are practically identical except for those of (3). At the moment, the effect 

 of couplings is of only incidental interest, and these results (i.e., (3)) are pre- 

 sented here primarily for later convenience. 



It must be emphasized that Gerritsma's tests do not go so far as Dalzell' s 

 in proving the validity of the superposition hypothesis. The irregular Vaves 

 used by Gerritsma are very mild by comparison. However, Gerritsma's use of 

 three methods of measurement — with his demonstration of their equivalence — 

 is of far-reaching importance. In a direct way he has proved the usefulness and 

 validity of the old procedures of testing in regular waves. Secondly, since these 

 ordinary frequency response investigations are appropriate tools for studying 

 ship motions in random seas, other methods of characterizing the system should 

 be equally valid if such methods are equivalent to finding the f.r. functions. In 

 particular, the measured response of a ship to a single transient wave can yield 

 as much information as a long sequence of regular wave tests. Moreover, such 

 a test is purely deterministic, and there are none of the special difficulties which 

 are so characteristic of tests in random seas (real or artificial). 



I have been consistently restricting myself to consideration of heave and 

 pitch motions, but this section would be lacking without some mention of recent 

 work on the problem of superposing ship roll responses. One is inclined to be- 

 lieve intuitively that roll motion will involve stronger nonlinearities than other 

 ship motions, and regular wave experiments seem to confirm this intuitive feel- 

 ing. Nevertheless, at least two papers have appeared which present irregular 

 wave test data indicating that roll responses can indeed be superposed in the 

 same sense as heave and pitch responses. 



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