motion of the breakwater along the y-coordinate axis, and roll is the 

 rotation about the long axis or the z-coordinate direction. 



As long as the problem is linear, computing the performance of a 

 floating breakwater may be separated into three parts: 



(a) Formulate equations of motion. 



Calculate hydrostatic forces and moments. 



Evaluate hydrodynamic coefficients in equations of motion. 



Compute exciting forces on breakwater. 



Solve for the motions and motion-generated waves . 



Compute forces in the mooring lines. 



(b) Solve for the waves diffracted by a rigidly restrained 

 breakwater. 



(c) Sum components to obtain total reflected and total trans- 

 mitted waves. 



When combined, these parts of the calculation provide complete 

 performance data for a two-dimensional breakwater. 



a. Breakwater Motions . In deriving the equations of motion, 

 Newton's law is used. 



ra. . a. = E forces; CI) 



here: 



a. = motion of the breakwater in sway, heave, and roll for 



i = 1,2,3, respectively. The dot above indicates differen- 

 tiation with respect to time. 



m. . = mass or mass moment of inertia when i = j and zero when i ?^ j , 



Expanding this equation to include the various forces in the summa-- 

 tion yields : 



n. . a. = F. (inertial) + F. (wave damping) 



+ F. (friction) + F. (hydrostatic) + F. Cmoo^ing) 

 + F . (wave exciting) 



15 



