c. Procedure When a Is Greater Than 80° — The R/J Method . In any depth, 

 when a becomes greater than 80°, the above procedure cannot be used. The 

 orthogonal no longer appears to cross the contours, but tends to run almost 

 parallel to them. In this case, the contour interval must be crossed in a 

 series of steps. The entire interval is divided into a series of smaller 

 intervals. At the midpoint of the individual subintervals, orthogonal angle 

 turnings are made. 



As can be seen in Figure 2-21, the interval to be crossed is divided into 

 segments or boxes by transverse lines. The spacing R of transverse lines is 

 arbitrarily set as a ratio of the distance J, between the contours. For the 

 complete interval to be crossed, C /C is computed or found from Table C-4 of 

 Appendix C (C^/C , not C /C ) . 



J : Distance between contours at turning points,* 



R : Distance along orthogonal 



T = 12 s 



Lq: 737 ft 



For contour interval from 40folh to 30foth C /C = 1.045, C /C =0.957 



12 '21 



A X : 2<'-25 



Figure 2-21. Refraction diagram using R/J method. 



On the template (Fig. 2-18), a graph showing orthogonal angle turnings 

 Aa is plotted as a function of the C /C value for various values of the 

 ratio R/J. The Aa value is the angle turned by the incoming orthogonal in 

 the center of the subinterval. 



The orthogonal is extended to the middle of the box, Aa is read from the 

 graph, and the orthogonal turned by that angle. The procedure is repeated for 

 each box in sequence, until a at a plotted or interpolated contour becomes 

 smaller than 80°. At this point, this method of orthogonal construction must 

 be stopped, and the preceding technique for a smaller than 80° used; other- 

 wise, errors will result. 



d. Refraction Fan Diagrams . It is often convenient, especially where 

 sheltering landforms shield a stretch of shore from waves approaching in cer- 

 tain directions, to construct refraction diagrams from shallow water toward 

 deep water. In these cases, a sheaf or fan of orthogonals may be projected 



2-70 



