Ogilvie 



we do not need to shift the data window or the output. Wj, Wj and W3 are the 

 windows which are explained later. Otherwise, \}i(co)\ will be underestimated 

 by more than 5%. sAt should also be chosen so as to satisfy 



|sAt| < 0.05 NAt . 



Otherwise, adopt y(t + sAt) as y(t). This is the clear solution for the elimina- 

 tion of the effect of windows on frequency response function. 



For example for roll, expressed by the equation of motion, 



where 



+ 2k(^6+ aj^4> = co^yC'^) —- ^(c^) e 



7(0)) is the effective wave slope coefficient and 



— i(a>) e ^ is the wave slope expressed by the wave height U^) measured 

 at the C.G. of the ship. 



The amount of time shift is computed as follows: 



m^) 



{a? - co^) + (2kco CO)- 



-2kco co^ 

 cx(co) - tan'^ ( ^— I + 



da( o)) _ d 

 dco dco 



tan' 



■2kcl>m 



■2kco (w 2 + o)^) 



(0)2 -a;2)2 + (2/<o; o)): 



therefore 



C.G. 



^ 



WAVE 



MEASURING 



POINT 



Figure 4 



da( CO) I ]_ 



doj KCO 



0)=CtJ o 



o 



Namely if we want a good estimate (with small 

 bias) of H(o)), the amount of shift sAt is 



1 



sAt = -7— . 



KCl> 

 O 



This shows that the output of roll y(t + sAt) 

 should be taken as y(t). When the wave height 

 i(co) is measured at the distance, D, as is 

 shown in Fig. 4, the phase difference between 



102 



