SHIP MOTIONS 



167 



20 



o 



■20 





2.0 



3.0 



4.0 



5.0 



e.o 



7.0 



8.0 



Fig. 7 Analysis of pitching and heaving of a ship model in irregular waves (from luchs and MacCamy, 1953) 



111 the .statistical troatnieiit of waves, Section 1-8, sea 

 conditions were assumed to lie stationary: i.e., the sta- 

 tistics of the waves remain unchanged with translations 

 in time and/or space. In reality, wave conditions change 

 rather slowly with resjiect to the observation time and 

 under such conditions the change in the seaway mav be 

 approximated by a succession of discrete stationary 

 events. Ship motions, since they result from such .sta- 

 tionary sea conditions, are considered (and are oliserved) 

 to be likewise stationaiy and are treated as such. The 

 deterministic mcthoil does not require the stationary as- 

 sumption, but like the statistical approach, interpreta- 

 tion of nonstationary events produced by nonstatioiiary 

 events is a problem of no small magnitude. 



.\ deterministic method of calculating ship i('si>on.-<c 

 will be discussed in the next subsection. The bulk of this 

 section will be devoted to the review of statistical meth- 

 ods of treating ship motions, because almost all research 

 effort to date has been in this direction and it appears to 

 be the most fruitful approach at this time. 



3.2 A Deterministic Method for Studying Ship 

 Motions in Irregular Seas. The only known deterministic 

 treatment of sliij) res|)onses is due to Fuchs (1952) and 

 Fuchs and MacCamy {\\)\i.\) based on previous work by 

 Kreisel (194,5). 



Fuchs' (1952) paper pntvides the mathematics for es- 

 talilishing the relationship between two simultaneously 

 occurring phenomena. Following Kreisel, the relation- 

 ship between the surface wa\e elevation and the pressure 

 record measured at a certain water depth is discussed. 

 The relationship between wave elevations at two nearby 

 points, the forces acting on piles, and motions of a rec- 

 tangular block in waves are also discu.s.sed. In Fuchs 

 and MacCamy 's (1953) and Fuchs' (1954) papers, these 

 mathematical methods are applied to a ship's hea\-ing 

 and pitching motions at zero speed in irregular long- 

 crested waves. The pha.se relationships, as well as the 

 amplitudes of motions, are e\'aluated. 



The work of Fuchs and MacCamy is a spci-ial case of 

 the earlier (1952) work of Fuchs in linear-prediction 

 theory. Fuchs' tlieoiy is extended to acconun<nlate 

 irregular waves and thereby results in the less general 

 linear case. Their treatment is best described by the 

 following quote from their 1953 paper: "...the oscilla- 

 tions of a ship in a complex system of progressix-e waves 

 of small .steepness can be expressed as the com'olution 

 type integral of the recorded wave motion and a kernel 

 function which is the Fourier integral of the response of 

 the ship to a sinusoidal forcing function. Kernels for 

 pitching and hea\ ing are computed explicitly for a freely 



