To illustrate how values of Qa^' Ho listed in Table 4-11 were 

 calculated, the value of Qa^, H^ ■'■^ here calculated for H^ = 1 and 

 the north direction, the top value in the first column on Table 4-11. 

 The direction term, FCa^) , is averaged over the sector from a = 67.5° 

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

 F(aci) is found to be 0.261. H^ to the 5/2 power is simply 1 for this 

 case. The frequency given in Table 4-10 for H^^ = 1 and direction = 

 north (NW to NE) is 9 percent or in decimal terms, 0.09. This is mul- 

 tiplied 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. Put- 

 ting all these values into Equation 4-42 gives 



Qf^j = 1.373 X 10^ (0.045) (1)^2 (0.261) 



= 1,610 yd.Vyr. (See Table 4-11) 



Table 4-11 indicates the importance of rare high waves in determin- 

 ing the longshore transport rate. In the example, shoreward moving 8- foot 

 waves occur only 0.5 percent of the time, but they account for 12 percent 

 of the gross longshore transport rate. (See Table 4-11.) 



Any calculation of longshore transport rate is an estimate of poten- 

 tial longshore transport rate. If sand on the beach is limited in quan- 

 tity, then calculated rates may indicate more sand transport than there 

 is sand available. Similarly, if sand is abundant, but the shore is 

 covered with ice for 2 months of the year, then calculated transport 

 rates must be adjusted accordingly. 



The procedure used in this example problem is approximate and 

 limited by the data available. Equation 4-42, and the other approxi- 

 mations listed in Table 4-11, can be refined if better data are avail- 

 able. An extensive discussion of this type of calculation is given by 

 Walton (1972). 



Although this example is based on shipboard visual observations of 

 the SSMO type (Section 4.34), the same approach can be followed with 

 deepwater data from other sources, if the joint distribution of height 

 and direction is known. At this level of approximation, the wave period 

 has little effect on the calculation, and the need for it is bypassed as 

 long as the shoaling coefficient (or breaker height index) reasonably 

 satisfies the relation (Kg)^/^ = 1.14. (See Assumption 2d, Table 4-9.) 

 For waves on sandy coasts, this relation is reasonably satisfied. (e.g., 

 Bigelow and Edmondson, 1947, Table 33; and Goda, 1970, Figure 7.) 



4.534 Enyirical Prediction of Gross Longshore Transport Rate (Method 4) . 

 Longshore transport rate depends partly on breaker height, since as 

 breaker height increases, more energy is delivered to the surf zone. At 

 the same time, as breaker height increases, breaker position moves off- 

 shore widening the surf zone and increasing the cross-section area through 

 which sediment moves. 



4-107 



