The deepwater wave velocity, C^ , can be approximated by (see eq . 2.37 

 in Wiegel, 1964) 



gT 

 C^ = 2 ~ 5.12 T (feet per second) 



(A-33) 



Using this along with equations (A-8) , (A-11), and (A-22) , the third expression 

 for P^g can be obtained from equation (A-20) : 



Us \ cos a 



''^ (5.12 T) i (8 H^)(2 cos a, sin a,) 



= 20.5 T H^ cos a sin a, (foot-pounds per second per foot) (A-34) 

 o o b ^ ^ ^ ^ ' 



This is equation (4-37) in the SPM. 



The final equation for Pj^, equation (A-21), reduces to 



/cos a \_i / V 



\s - 2(8.02 H^/2) y-^^^ 5.12 tJ (8.02 H^/^) (g h^) (^i cos a^ sin a^j 



= 100.5 I — \ cos a, sin a (foot-pounds per second per foot) (A- 35) 



by use of equations (4), (A-8), (A-11), (A-22), and (A-33). The cos a, term 

 in many cases, is close enough to 1.0 to be ignored. Therefore, equation (A-35) 

 can be further reduced to : 



P = 100.5 I — I sin a (foot-pounds per second per foot) 



(A-36) 



This is equation (4-38) in the SPM. 



The four approximate equations for P 



£s 



(eqs. A-28, A-32, A-34, and A-36) 



are given in Table 4-8 of the SPM. Unlike the four exact equations (P^ in 

 Table 4-7), these approximations are not equivalent, due to the different 

 assumptions made in deriving them. Trial solutions of all four approximations 

 suggest that they give values of P^ that agree within a factor of 2. Figures 

 4-36 and 4-37 in the SPM show that variation of Pj^g by a factor of 2 is within 

 the scatter of the data defining the dependence of Q on Pj^g . 



All results in this appendix, including the P£g approximations, are for 

 a coast with straight, parallel (but not necessarily evenly spaced) contours. 

 All results assume no friction loss, which may become an important omission 

 for waves traveling long distances over shallow, flat slopes (Bretschneider 

 and Reid, 1954; Walton, 1972). Additional assumptions used in the derivations 

 are siommarized in Table 4-9 of the SPM. The essentially approximate basis 

 for the longshore transport prediction must be recognized when the energy flux 

 method is used. The more that the prototype conditions agree with the conditions 



23 



