y F (0.) sin 6. I sin 6. I 



. ^, OV 1 1 ' 1 ' 



1=1 



n 



I (sin e I sin 6 1)2 

 i=l 



CA48) 



With these relationships, the corresponding values of the parameters 

 Ct, (J), k, C^, and Cp in the vertical wave force equation which best 

 fit the data throughout the complete wave cycle can be obtained. 



The coefficients of mass and drag, C^ and Cp, are obtained directly 

 from the parameters D.. and E, , since 



Mv 



y F (6.) cos 6. 



.^T OV 1 1 



1=1 



n 



F,, y cos^ 6. 

 Mv . ^ , 1 

 1=1 



(A49) 



n 



y F (6.) sin 0. Isin 6. I 

 E .^ OV 1 1 ' i' 



C„ = - TT^ = - ^-^ . (ASO) 



D 



Dv 



n 



F_ y (sin 0. Isin 6. 1)' 

 1=1 



Since A^ = 1/2 C^ F, cos 2(^ and B^ = 1/2 Ct F^.^ sin 2()), the phase 

 shift parameter (}> can be obtained from: 



1/2 (2(j)) = 1/2 tan" 



■1 l^llL^] = 1/2 tan-^ U 

 |_cos 2^J [A, 



since 1/2 C. F cancels out of the expression \j—\- Thus, 



1/2 tan"^ ^ 



n 



y F (6.) sin 29. 

 i=l °^ ^ V 



/y sin^ 26. 

 i=l 



n 



y F (6.) cos 26. 



^i=l °^ ^ V 



/y cos^ 26. 

 i=l 



(A51) 



(A52) 



133 



