Evaluation of Motions of Marine Craft in Irregular Seas 



of incident frequency. Integration required to obtain the impulsive response 

 functions would undoubtedly have to be done by computer since the transfer 

 functions with frequency-dependent coefficients are very complicated. 



An attractive alternative to theory is the use of experimentally determined 

 responses of a model of the vessel to either regular or irregular waves. It is 

 now a routine procedure to obtain from towing tank tests the amplitude response 

 operators and their respective phases at selected values of frequency. In such 

 tests the motions are related to wave measurements made by wave wire or 

 other devices placed ahead of the model or abeam in time with amidships. It 

 can, therefore, be appreciated that these transfer functions (obtained by graph- 

 ing amplitude and phase response against incident frequency) are indeed depend- 

 ent upon the location of the wave wire. It is often found that the impulsive re- 

 sponse function derived from such data exhibits values other than zero for 

 negative values of time t in distinction to completely mechanical or electrical 

 systems for which it is known that K(t) = for t < . It is intuitively clear 

 from physical concepts that the ship (or model) will respond to a wave before 

 the crest (say) reaches the bow because of the spatial distribution of both the 

 ship and the pressure field of the wave. It will be shown in the following section 

 how the extent of the part of K(t) for negative t can be reduced by judicious 

 positioning of the wave measurement with respect to the model. In any event, it 

 will be necessary to have some "future" information of the wave in order to 

 compute the present time motion for all cases in which the vessel is of length 

 comparable to the exciting waves. 



For those interested in applying this technique, it is appropriate to indicate 

 in some detail how the impulsive response function for any mode of motion may 

 be obtained from data obtained from a model in (a) regular waves and (b) irreg- 

 ular waves. 



K(t) from Regular Wave Tests 



If one regards the regular sea motion (in a towing tank experiment) as the 

 input 



and one records the output of any mode of the model motion as 



x(t) = 1 77^ I A(aj) sin ["ojt - cp(a;)l 



where cp(aj) is the phase angle referenced to the wave and h{cS) is the amplitude 

 response of the model in a particular mode, then the transfer function or com- 

 plex response function per unit amplitude of input is identified as 



<D(aO = A(a;) e'^^^'^ (41) 



Upon completion of a plot of A(aj) and cp(w) for enough discrete values of a so 

 that smooth curves may be drawn to define both Ac^o and fo(a) , one may then 

 find the impulsive response function by applying the operation 



471 



