7-19), the integration indicated in Equations 7-20 and 7-21 «iay be per- 

 formed if the upper limit of integration is zero instead of n. This 

 leads to 



1 , /27rd\ / 27rt 

 K. =-tanh \-^jsin \- — j , ^7.26) 



1 / 47rd/L \ , /27rt\, /27rt\ 



- - n Icos ^— yl ^°s \-^ 



_ 1 — cosh [27rd/L] 



^'" ~ ^ ^ (27rd/L) sinh [27rd/L] ' ^^"^^^ 



_ ]_ J_ / 1 1 - cosh [4ird/L] 



^ 2 2ny2 (47rd/L) sinh [47rd/L)y ■ (7-29) 



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

 Equations 7-26 and 7-27, the maximum values of the various force and 

 moment components may be written 



(7-30) 

 (7-31) 

 (7-32) 

 Mflm = ^Dm ^ S^ . (7-33) 



where K^^ and K^)^ according to Airy theory, are obtained from Equations 

 7-26 and 7-27 taking t = -T/4 and t = 0, respectively, and S^ and S^ 

 are given by Equations 7-28 and 7-29 respectively. 



Equations 7-30 through 7-33 are general. Using Dean's stream- function 

 theory (Dean, 1973), the graphs in Figures 7-43 through 7-46 have been 

 prepared and may be used to obtain Kim> ^Dm> ^im and S^. S-i, and 

 S^, as given in Equations 7-28 and 7-29 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 S^ depend 



on phase angle; Figures 7-45 and 7-46 give maximum values, S-im and Som. 

 The degree of nonlinearity of a wave can be described by the ratio of wave 

 height to the breaking height, which may be obtained from Figure 7-47 as 

 illustrated by the following example. 



7-75 



