Ogilvie 



z(t), and v//(t) will probably have values for their coherency which are 

 appreciable, perhaps, 0.6 to 0.8. However, the oncoming apparent waves 

 will at one time be high on the port side and at another time be high on 

 the starboard side causing the vessel to roll first one way and then the 

 other for the same apparent wave form in rj^(t). More precisely, 

 c^(co^,j^) and qJco^,e^) in (11) will be odd as a function of 0^- Hence 

 both C^^(«e) ^^^ %^(<^e^ ^^^^ ^® zero. This implies that the coheren- 

 cies between rj(t) and 0(t), z(f) and 0(t), and >/'(t) and 4>(t) will all 

 be near zero in a practical case when the motions are observed in head 

 seas. 



During storms, when in a hove to condition, ship masters prefer to 

 take the seas a few points off the bow instead of from directly ahead. As 

 explained to the author by a naval officer, this is because the vessel tends 

 to roll in a more favorable way so that less green water is shipped over 

 the bow. The side of the vessel toward the oncoming sea as explained 

 by the above considerations will roll away from an oncoming crest as the 

 bow rises and thus less water will be shipped. Stated another way, the 

 coherency between T7^(t) and <^(t) will be increased in a way favorable 

 to drier decks. 



A similar analysis can be carried out for a ship underway in beam 

 seas. Roll, heave, and Ve(^) will have fairly high coherencies. Pitch 

 will be nearly incoherent with the other three components of the vector 

 process. 



Since these statements in 1957, our knowledge of the directional wave spec- 

 trum has been improved by the results of Longuet-Higgins, Cartwright and 

 Smith (1963), by the results of Cartwright and Smith (1964) and by the results 

 that I have described in another paper in this volume. The above conclusions 

 have been verified by two papers that have been written since the report was 

 prepared. The first paper that verified these conclusions is one by Canham, 

 Cartwright, Goodrich, and Hogben (1962). In this paper, the ship was operated 

 on an octagonal course. The forcing seaway was measured on this ship, not ex- 

 actly at the center of gravity but this is irrelevant, and the various motions 

 were also measured. It was indeed a fact that the coherency of roll and the 

 forcing seaway was very small in head seas and that the coherency of pitch with 

 the forcing seaway was very small for beam seas as predicted. 



The important point is that this is to be expected. It is a basic feature of 

 the probability model. The result does not mean that there is something wrong 

 with the records of roll and pitch under these circumstances, and it does not 

 mean that the theory is in error. For short crested waves the situation is more 

 complicated than it is for ships in long crested waves. 



In another study, O'Brien and Muga (1965) measured the response of a 

 moored aircraft carrier to forcing waves and obtained spectra and co-spectra 

 that yielded coherencies consistent with the above conclusions. 



The above results on spectral and co-spectral coherencies can be analyzed 

 in such a way as to provide an understanding of many features of ship motions 



86 



