The expression for the force F^y]^ of Equation (2) is obtained by 

 integration of Equation (1) over the submerged length of the form. 

 Following reference (1), with coordinates as shown in Figure 3, leads to 

 the expression: 



cyl 



where 



16 



2nd ' 

 L 



4nd ^ 

 L 



2Tttn 



-1 



1 - e 



1 - e 



(3) 



(4) 



and H = Wave height 

 L = Wave length 

 T = Wave period 



d = Mean wetted length of form 

 g = acceleration due to gravity 

 t„ = Time the maximum force leads the wave crest. 



Consistent with the assumption of the Airy wave theory the expression 

 for the velocity that was used in obtaining expression (3) is i-^ 



i T 



2ttz 

 L 



2:Tt 

 T 



(5) 



The negative sign appears in expression (4) for d^^ the angle between 

 the maximum force and the wave crest, because the force always leads 

 the wave and 6^^ will therefore be in the fourth quadrant. 



Momentum Change Caused by Net Force 



In evaluating the effect of the wave force on the hydrodynamic form 

 it is necessary to consider the momentum change due to this force in a 

 wave period. Accordingly: 



.2n 



A(Mv) = f- r F(d) d 9, 



(6) 



46 



