and the interpolated value of F^ is: 



(Fj^)j^ = Wl(Fi^)l + Wu(Fi^)u 



= (0.744) (4.90) + (0.256) (6.10) 

 = 5.21 



To evaluate this interpolated value, a Stream-function solution was developed for the 

 conditions of interest, and Fjj from the actual solution was found to be 5.04 or a difference 

 of about 3.4 percent. 



More comprehensive evaluations of the accuracy of the interpolation method are 

 presented in the next example. 



Example 7-b— Assessment of the Interpolation Method 



To present a more extensive evaluation of the accuracy of the interpolation method, two 

 special cases (one shallow -water and one deepwater) were selected for evaluation. The wave 

 characteristics for these two cases are presented in Table R. 



TABLE R 



Wave Characteristics Selected for Accuracy 

 Evaluation of Interpolation Method 



Case 



Wave Height, 

 H(ft) 



Wave Period, 

 T (sec) 



Water Depth, 

 h(ft) 



S-1 

 (Shallow Water) 



S-2 

 (Deep Water) 



19 

 44 



20 

 10 



30 

 160 



Using the procedure described, interpolated values of a number of quantities of interest 

 were developed and compared with values obtained by Stream-function solutions at the 

 wave conditions of interest. Table S presents a summary of the percentage differences 

 between the solution and interpolated values. 



As an overall statement regarding the interpolation, it is noted that Table S indicates that 

 the procedure presented generally provides results which are within 5 percent; however, 

 differences up to 10 percent could occur. One final comment concerning the consistency of 

 the tabulated values is in order. In preparing the auxiliary plots, it was usually found that a 

 line could be drawn through the four points within 2 to 3 percent, except for the breaking 



93 



