Substituting the approximations represented by equations (4) , (A-22) , and 

 (A-27) into equation (A-9) yields P^g approximations for each of the four 

 equations for P„ in Table 4-7. 



Equation (4-31) for P^ in Table 4-7 of the SPM is approximated by 



P„ * 2(8.02 Ul'^) X (8 h2) sin 2a, 

 Us ^ b ■' 4 ^ b-' b 



=32.1 H^/^ sin 2a, (foot-pounds per second per foot) (A-28) 



which involves only height and direction at the breaker. This is equation 

 (4-35) of Table 4-8 in the SPM. 



In the same way, equation (4-32) for P^^ (eq. A-19) can be reduced to 



1/2 2 

 P„g = 16.0 H, H sin 2a (foot-pounds per second per foot) (A-29) 



Hjy is put in terms of H^ using equations (A-10) and (A-11) to get 



h1/2 = { Z\ (K H )l/2 (A-30) 



In this equation, cos a, equals 1.0 to a good approximation. For example, 

 even if a-^ has a high value of 20° (exceeded less than 5 percent of the time 

 on straight beaches), (cos 20°)^/'+ = 0.98. 



So, using this approximation and substituting equation (A-30) into equation 

 (A-29), 



P„ = 16.0 H^'2 (cos a )!/'+ K^''2 g^j^ 2a (foot-pounds per second 



per foot) (A-31) 



The shoaling coefficient. Kg, is approximated by the breaker height index. 

 H^/py , obtained from the experimental work of Iversen (1952). Related data are 

 in Figure 2-65 of the SPM. H^ is the unrefracted- deepwater water height. If 

 the slope and period are known, a steepness can be computed, and Hj,/H' obtained 

 from these experimental results. However, the period in offshore wave statistics 

 correlates poorly with the littoral wave period (Harris, 1972). A reasonable 

 approximation without using the period is obtained by observing that %/H' 

 ranges from 0.95 to 1.7 for plunging and spilling waves, a center range of about 

 1.3 for expectable slopes and moderately steep waves. Therefore, Kg is assumed 

 here to be 1.3. Since Q depends on the square root of K , this assumed 

 value will usually give Q to within 10 percent of the value from Iversen 's 

 data when steepness and slope information is available. 



This approximation reduces equation (A-31) to a convenient approximation 

 involving only deepwater height and direction, which is equation (4-36) in the 

 SPM: 



P„ = 18.3 H^''2 (cos a )!''+ sin 2a (foot-pounds per second 



per foot) (A-32) 



22 



