Evaluation of Motions of Marine Craft in Irregular Seas 



(a) "Shift" the wave input from <f j to ^^ so that it may then be convoluted 

 with the K(t) determined for waves measured at '^^; or 



(b) "Shift" the K(t) from ^^ to ^j . 



Step (a) is accomplished by convo luting the given wave record with K^ given by 

 (55) and then convolve that result with the system K(t) to obtain the response. 

 Step (b) is accomplished by modifying the transfer function from which K(t) is 

 computed by the factor 



e ^ 



(taking care to apply the correct sign to the exponent!) and thence to compute a 

 new K(t) which can be convoluted with the given wave record. 



APPLICATIONS OF IMPULSIVE RESPONSE TECHNIQUE 

 TO PREDICT SfflP MOTIONS IN IRREGULAR SEAS 



The previous sections of this paper have discussed the significance of the 

 impulsive response function and have described its application in determining 

 the time history of ship motions in irregular seas. During the past several 

 years, the Davidson Laboratory has employed this technique to evaluate the mo- 

 tions of a variety of marine craft operating in random seas. The results of these 

 applications will be summarized and discussed. 



Displacement Ship in Head Seas 



In 1961, Fancev [13] used the impulsive response technique to determine 

 the time history of heave and pitch motion of a destroyer model in irregular 

 long-crested head seas. The model used in the experiments was the DD692 

 Class Destroyer (long hull). The full-scale ship is 392 ft long, has a beam of 

 40.83 ft and has a displacement of 3471 long tons in salt water. The model was 

 tested in moderately high, irregular, long-crested head waves that had a broad 

 energy spectrum. The average height of the waves was about 1/60 of the model 

 length. Measurements were made of the wave elevation (at a constant distance 

 forward of the model LCG), pitch angle, heave at the LCG and bending moment 

 amidship. Dalzell [3] reported the results of these tests and, by the method of 

 cross- spectral analysis, derived the transfer function of the destroyer for a 

 wide range of speeds. It will be recalled from Eq. (21) that the transfer function 

 0(0)) is written: 



<|)(aj) = A(co) e"^**^"^^ = P(co) + iQ(a)) 



where 



P(co) = A(co) COS [4)(co)] 

 Q(cj) = -A(oS) sin [cpCa))] 



477 



(57) 



