sinh (^) 



(A653 



^2 = - ^M %i = Cm P V (|^) (A66) 



max 



2Trz. 

 max T smh (— j — ^J 



Thus, the total horizontal wave force at any position 0^^ in the wave 

 cycle can be expressed as : 



Fh (6i) = CFd)^ - CFl)h 



= A2 cos e^ I cos Q^\ + B2 sin 9^ (A68) 



where the parameters A2 and B2 are constant for any given values of Cr, 

 and C^, corresponding to the particular wave and pipeline conditions 

 under consideration. 



The sum of squares of the differences between the observed horizontal 

 forces, FqJ^ (9i), and the corresponding calculated forces, Fj^ (9^), is 

 written as: 



I [Fh (0i) - Foh f^i^]' = I [^2 c°s Bi I cos 0i 

 i=l i=l 



^2 sin 6^ - F^^ (9^)]^ (A69) 



The derivatives of this expression taken with respect to the unknown 

 parameters A2 and B2 and set equal to zero give the following equations: 



[Fh (Si) - Foh C6i)]^ , 

 ^vr- ■ = 2 A„ (cos 6- cos 9- )' 



137 



