^ ^ , 1 - cosh [2Trd/L] 



i (2TTd/L) sinh [2TTd/L] 



(7-35) 



1 - cosh [4ird/L] 



s =l + L. 1 + 



D 2 2n \ 2 (4iTd/L) sinh [Aird/L) 



(7-36) 



where n = C~/C has been introduced to simplify the expressions. From 

 equations (7-33) and (7-34), the maximum values of the various force and 

 moment components can be written 



T7D 



^im = Cm Pg -ZT » ^i 



■m 



(7-37) 



Fz)m = ^ i P8 D h2 K^ 



(7-38) 



^m = ^im d S^ 



(7-39) 



%„, = Fz?m 'I % 



(7-40) 



where K^;^ ^^^ ^^^Dm according to Airy theory are obtained from equations 

 (7-33) and (7-34) taking t = -T/4 and t = , respectively and S- and 

 %) are given by equations (7-35) and (7-36) respectively. 



Equations (7-37) through (7-40) are general. Using Dean's stream-function 

 theory (Dean, 1974), the graphs in Figures 7-71 through 7-74 have been pre- 

 pared and may be used to obtain K^„ , I^ , S^^ , and Sr. . S- and ^ , 

 as given in equations (7-35) and (7-36) for Airy theory, are independent of 

 wave phase angle 6 and thus are equal to the maximum values. For stream- 

 function and other finite amplitude theories, S; and Sq depend on phase 

 angle; Figures 7-73 and 7-74 give maximum values, S^^ and ^^ . The degree 

 of nonlinearity of a wave can be described by the ratio of wave height to the 

 breaking height, which can be obtained from Figure 7-75 as illustrated by the 

 following example. 



*************** EXAMPLE PROBLEM 19************** 



GIVEN: 



A design wave H = 3.0 m (9.8 ft) with a period T = 8 s in a 



depth d = 12.0 m (39.4 ft) . 

 FIND : The ratio of wave height to breaking height. 



SOLUTION : Calculate 



d 12.0 



= 0.0191 



2 2 



gl (9.8) (8) 



7-112 



