Prediction of Ship Slamming at Sea 



/,) ■' ab 



Qab(^e) = - -^ Q"J^e) (A.5) 



1 



The value of the correlation coefficient, p^^ , depends on the relative posi- 

 tion of the two points A and B. As will be shown later in Table 4, if point A is 

 located near the ship bow and point B is located near the midship, the correla- 

 tion coefficient is very small for conditions severe for slamming. This means 

 that the motions at these points (ship bow and midship) are statistically almost 

 uncorr elated, and thereby the second term of Eq. (A. 3) can be neglected prac- 

 tically. 



The correlation coefficient, p^^, can be obtained by a formula similar to 

 that for the coefficient p^^. That is. 



- ^"''wx _ /(/C,x(^e)d^e)' + (l%.(^e^d^e)' (A.6) 



^"' ' ^w^x "1/ J3>^w('-e)d-e /^xxC-Jd- 



where 



C^^(w^) = energy density of cospectrum, i.e., energy density of the real 

 part of the cross- spectrum of wave and vertical ship motion, 



Qwx(^^e^ - energy density of quadrature spectrum, i.e., energy density of 

 the imaginary part of the cross- spectrum of wave and vertical 

 ship motion, 



$^^(a)g) = energy density of the auto-spectrum of wave, 



^xx('^e^ ~ energy density of the auto-spectrum of motion. 



If the wave is measured not at the same location at which the bow motion is 

 measured but at a certain distance ahead of the model (as is illustrated in Fig. 

 21), then the following phase correction due to the distance between wave probe 

 and point X is required in the evaluation of the cross- spectrum 



tLl (A.7) 



wx 



where 



*wx('^e) - cross spectrum between wave and vertical ship motion at 

 point X, 



583 



