where f is the decimal frequency, which is the percent frequency in Table 

 4-12, divided by 100. The constant A is of the type used in equation 

 (4-50). 



Since the available data are a and H_ , the appropriate equation for 



P. is given in Table 4-10. If A = 1290 , as in equation (4-50a), and 

 equation (4-45) in Table 4-10 are used, 



Q „ = 2.03 X 10^ fH ^'^^ Ffa 1 (4-54) 



o' o 

 where 



'(%) ■ [i 



cos a 1 sin 2a (4-55) 



This direction term, F(°'^) » requires careful consideration. A compass 

 point direction for the given data (Table 4-12) represents a 45-degree sector 

 of wave directions. If F(%) is evaluated at a = 45 degrees (NE or SE in 

 the example problem), it will have a value 12 percent higher than the average 

 value for F(a ) over a 45-degree sector bisected by the NE or SE 

 directions. Thus, if the data warrant a higher degree of accuracy, equation 

 (4-55) should be averaged by integrating over the sector of directions 

 involved. 



If F(a ) as evaluated at a = (waves from the east in the example 

 problem), then F(a ) = . Actually, a = degrees is only the center of 

 a 45-degree sector which can be expected to produce transport in both 

 directions. Therefore, F(a ) should be averaged over to 22.5 degrees 

 and to -22.5 degrees, giving F(a ) = ± 0.370 rather than . The + 

 or - sign comes out of the sin 2a term in F(a ) (eq. 4-55), which is 

 defined such that transport to the right is positive, as implied by equation 

 (4-32). 



A further complication in direction data is that waves from the north and 

 south sectors include waves traveling in the offshore direction. It is 

 assumed that, for such sectors, frequency must be multiplied by the fraction 

 of the sector including landward-traveling waves. For example, the fre- 

 quencies from N and S in Table 4-12 are multipled by 0.5 to obtain the 

 transport values listed in Table 4-13. 



To illustrate how values of Qa , „ listed in Table 4-13 were cal- 



o ti 



culated, the value of Qa , „ is here calculated for H^ = 0.5 and the 



north direction, the top value in the first column on Table 4-13. The 

 direction term, F(a ) , is averaged over the sector from a = 67.5 degrees 

 to a = 90 degrees; i.e., from NNE to N in the example. The average value of 

 F(a ) is found to be 0.261. H^ to the 5/2 power is 0.177 for this case. 

 The frequency given in Table 4-12 for H^ = 0.5 and direction = north (NW to 

 NE) is 9 percent, or in decimal terms, 0.09. This is multiplied by 0.5 to 

 obtain the part of shoreward-directed waves from the north sector (i.e., N to 

 NE), resulting in f = 0.09 (0.5) = 0.045 . Putting all these values into 

 equation (4-54) gives 



Q„ = 2.03 X 10^ (0.045) (0.5)^'^ (0.261) = 4220 cubic meters per year 



(see Table 4-13) 



4-103 



