where A(Mv) is the momentum change, F(0) is the wave force, and d = 2itt/T 

 with t the time. When the virtual mass force component exceeds the 

 viscous drag force component by at least 2.5 the viscous component can 

 be neglected'^ and relation (6) can be approximated as (utilizing 

 relation (2) ) : 



A(Mv) «^ 



from which, 



Jo ^cyl sin fl d + fj" (K + 1) F^^^ sin d d 



^^^ « - [^1 F 1 (7) 



where F -i is given by Equation (3) and K = 0.17. From Equation (3) it 

 can be seen that the ratio of the virtual mass force component to the 

 viscous drag force component is proportional to D/H. For large diameters 

 the viscous drag force component can be neglected up to fairly large 

 wave heights. For the case of the example presented below the form 

 diameter is 20 feet and, according to curves in reference (4), the 

 neglection is accurate to wave heights up to 60 feet. 



The momentum change per wave caused by the force on the hydrodynamic 

 form of Figure 1 is given in Figure 4. The effect of a 5 foot and a 

 10 foot wave for various wave lengths is shown. These curves were 

 obtained from relations (3) and (7) with Cj) = 1.6 and Cj^ = 1.5." In 

 order to lend a physical meaning, the momentum change that is caused by 

 a one knot and a one-half knot current flowing in the direction of wave 

 travel (into the convex side of the form) is also shown. At intersection 

 points between a wave force curve and a current curve the effect of the 

 crescent form is to cause an impulse that is equal in magnitude to the 

 impulse of the current drag force but opposite in direction; e.g., with 

 a wave of 10 foot height and 500 foot length and a one knot current the 

 net momentum change is zero and the net movement of the hydrodynamic 

 form under these conditions would be zero. The steady current flow of 

 one knot creates a drag force of 6480 lbs on the form which is equivalent 

 to approximately 20 hp. Therefore, with the particular wave condition 

 stated above, the hydrodynamic form extracts energy from the waves at 

 the net rate of approximately 20 hp."'' The sea state example taken is 

 in the range of seas classed as state No. 5 (rough sea). 



Based on references (5) and (6), Cd and Cj^ are considered not to vary 

 significantly with Reynolds number. 

 -kit 



Net energy rate refers to that energy available for net motion opposite 



to wave direction. 



47 



