Davis and Zarnick 



CO = y (x/b^ + 4k - b) , 



Phase angle of 6 



f, 4 



>. = 



Figure 1 



In addition various other simple relations can be derived for determining b 

 or k quickly. For example when the phase angle of the response d is exactly 

 90° with respect to the regular wave at frequency oj, then 



= ^/k , 



bx/k 



Similarly if the phase angle of e is exactly 45° then 



\/2(k-aj2) 72 (boj) 



* * * 



(3) 



(4) 



REPLY TO THE DISCUSSION 



M. C. Davis and E. E. Zarnick 



David Taylor Model Basin 



Washington, D.C. 



Mr. E, V. Lai tone is apparently unaware of some of the more recent devel- 

 opments in the area of ship motions. It has been known for some time that 

 second-order differential equations do not properly describe ship motions, par- 

 ticularly in the pitch and heave modes which we have concerned ourselves with 

 in our paper. This problem has been glossed over in the past by the use of fre- 

 quency dependent coefficients. The tests in waves are further complicated by 

 the fact that the wave height (referenced at the center of gravity) is defined as 

 the input to the system which results in a particular amplitude phase relation- 

 ship exclusive of any dynamics effects. Consequently, these data would not be 



542 



