9v 

 dt 



T2 . , ,27Td, 



smh (-^) 



cos 6, 



(A4] 



where 



H = wave height 



T = wave period 



L = wavelength 



d = Stillwater depth 



z = vertical distance above the bottom 



2TTt 



6 = —^ = position of the wave cycle with respect to time. 

 Substituting these expressions into the vertical force equation yields: 



t2 sinh i^-) 



- Cr 



+ c, 



pATQl 

 2T^ 



cos 6 



2ij2 smh (-r— ) 



. ,2 .2-nd^ 

 smh (— j— ) 



2 .27TZ. 



PATT^H^ cosh C-L-) 



27-^ 



. ,2 .2Trd, 

 smh (— f— 3 



[cos^ (9 - (()) - k] 



(A5) 



or 







^ = "S^Mv '^^^^ 



- CdFo^ sine 



1 sin 



where 



pV27T^H 

 *^Mv , 



smh i—~j 





smh (-^-3 





pAiT^H^ 

 PDv 2 

 2T 



. ,2 ,2ttz-, 

 smh^ (-^) 





smh (-j— ) 





+ ClFlv [cos^ (e - (})) -k], 



(A6) 



CA7) 



CA8) 



12.6 



