Thus, 



H = H^3 [^(f)]''' ^'"'^ 



The mean value, Hp , of the wave heights larger than H is, using 

 equations (B-7) and (B-8) , 



H = - C HP(H] dH 

 p p H ^ -^ 



= _g(H/Hp^s) ^°° ^^1 -(H/Hy,^g] I (B-10) 



H -* 



Integrating by parts, substituting equation (B-9) , and dividing through by 

 Hms give 



"rms "rms y^rms / " 



1 2 ,a -x^ , 

 1 - -— / e dx 

 /IT o 



(B-11) 



where a = [£.n(l/p) ] ^''^ and x = H/H^^g . The ratio of the significant wave 

 height, Hg, to the rms height is found by letting p = 1/3 (from the defini- 

 tion of Hg) , which gives 



H 



H 



— = 1.416 



/I = 1.414. Thus, 



■rms 



^ v^ (B-12) 



Hg' - 2 H^^ (B-133 



From equation CB-2) , E °^ H and from equation (A-9) of Appendix A, 

 ?£ °c E. This means that if the significant wave height is used to compute 

 E or Pj, , the result will be approximately twice what it should be using 

 the rms wave height. 



Since coastal engineers are more familiar with H than H^^^g , all long- 

 shore transport predictions in the SPM are designed so that Hg is used when 

 the equation requires a wave height. (To emphasize that the resulting P^g is 

 approximately twice the theoretical longshore energy flux, P£g is called the 

 "longshore energy flux faotov^' in the SPM.) The design equations in the SPM 



28 



