Finally, the parameter k can be obtained from C-r knowing the value 

 of Ct , since 



n 



Cl 



I Fov ce,] / 



L=l / n 



1/2 - -r—r~ = 1/2 - ^=^ '-^ . CA57) 



Thus, once the vertical wave forces on a pipeline are measured 

 experimentally, the values of the parameters Ct, (j), k, C^, and Cq of 

 the vertical wave force equation which best fit the data throushout the 

 entire wave cycle can be determined for the particular set of wave and 

 pipeline conditions tested. 



In an analogous manner, the least squares analysis car be applied 

 to the horizontal wave force data. Omitting the horizontrl force 

 associated with eddy shedding, the horizontal component of the wave- 

 induced force can be expressed as equation (2) : 



Ph = ihh * fPD)h = Cm P V If + 1/2 Cp p A u|u| . (2) 



The data from the horizontal force measurements show that the horizontal 

 eddy forces are insignificant in comparison to the horizontal drag and 

 inertial forces for the experimental conditions tested. 



Using linear wave theory, the horizontal components of the wave 

 kinematics with respect to time can be expressed as: 



,, cosh (— r— 1 



ttH ^ L ^ 



T . .2TTd, 



smh (— f — J 



cos 9 



, ,2ttz. 



^ T 2,, cosh (—: — ) 



du _ _ 2tt H ^ L -^ 



i smh (-r-) 



sin e. (A58) 



135 



