GIVEN : Longshore current velocities (v) , breaker heights (H^) , breaker 

 angles (a^j) , and the beach slope (m) determined onsite during a short 

 field evaluation (see Table 2) . 



Table 2. Field calibration data (from 

 Galvin and Savage, 1966) . 



Obsn. 



Hb 

 (ft) 



m 



(ft/s) 



1 



2 



0.03 



2.42 



2 



3.2 



0.026 



4.33 



3 



1.8 



0.029 



1.96 



4 



8 



0.026 



1.26 



REQUIRED : An equation that will predict wave-induced longshore currents for 

 the test site. 



ANALYSIS ; Because the linearity expressed in equation (1) has a firm theoreti- 

 cal basis in the concept of radiation stress (Longuet-Higgins, 1970), and 

 because according to this concept, v = whenever Hb = or at = 0, the 

 prediction line must pass through the origin (0, 0). So Model II must be used. 



Let 



Y = V 

 and 



X = m(gHb)^/2 sin 2 



^b 



Regress Y on X to determine the best estimate of the coefficient of 

 proportionality between X and Y. 



CORRECT RESULTS : 



Regression coefficient 



Correlation coefficient 



Standard error of 6 



Test statistic for 6 



Estimated residual variance Sy.^^ = 1.8 



CONCLUSION : The version of the Longuet-Higgins type equation that best fits 

 this problem site (based on available current data) is: 



B 



= 17 



r 



= 0.91 



S3 



= 4.6 



t 



= 3.7 



V = 17m(gH|3)l/2 sin 2a^ 



NOTE: Fitting the equation to the data in this example produces results closer 

 to those obtained with larger data sets (eq. 1) if the line is forced through 

 the origin rather than being fit strictly to the data without this constraint 

 (see Fig. 5) . 



16 



