and 



sin ^ [0.5(0.5)] = 14.5' 

 cos a = 0.968 

 cos a = 0.866 



From the geometry of the wave rays. 



■^R- 



\V" 



COS a \ l/,2 



kCos a 



0.866 ] 1/2 

 i0.968/ 



= 0.945 



Figure 2-19 shows the relationships between 

 Kn in graphical form. 



period, depth, and 



a. Procedures in Refraction Diagram Construction — Orthogonal Method . 

 Charts showing the bottom topography of the study area are obtained. Two or 

 more charts of differing scales may be required, but the procedures are iden- 

 tical for charts of any scale. Underwater contours are drawn on the chart, or 

 on a tracing paper overlay, for various depth intervals. The depth intervals 

 chosen depend on the degree of accuracy desired. If overlays are used, the 

 shoreline should be traced for reference. In tracing contours, small irregu- 

 larities must be smoothed out, since bottom features that are comparatively 

 small with respect to the wavelength do not affect the wave appreciably. 



The range of wave periods and directions to be investigated is determined 

 by a hindcasting study of historical weather charts or from other historical 

 records relating to wave period and direction. For each wave period and 

 direction selected, a separate diagram must be prepared. C1/C2 values for 

 each contour interval may then be marked between contours. The method of com- 

 puting C1/C2 is shown by Table 2-2; a tabulation of C1/C2 for various 

 contour intervals and wave periods is given in Table C-4 of Appendix C. 



To construct orthogonals from deep to shallow water, the deepwater direc- 

 tion of wave approach is first determined. A deepwater wave front (crest) is 

 drawn as a straight line perpendicular to this wave direction, and suitably 

 spaced orthogonals are drawn perpendicular to this wave front and parallel to 

 the chosen direction of wave approach. Closely spaced orthogonals give more 

 detailed results than widely spaced orthogonals. These lines are extended to 

 the first depth contour shallower than I-q/'^- where 



O ^T^ 



b. Procedure When a Is Less Than 80° . Recall that a is the angle a 

 wave crest makes with the bottom contour. Starting with any one orthogonal 

 and using the refraction template in Figure 2-18, the following steps are per- 

 formed in extending the orthogonal to shore: 



( 1) Sketch a contour midway between the first two contours to be 

 crossed, extend the orthogonal to the mldcontour, and construct a 

 tangent to the midcontour at this point. 



2-66 



