(c) Rotate the template about the turning point until the C2/C2 value 

 corresponding to the contour interval being crossed intersects the tangent 

 to the midcontour. The orthogonal line on the chart now lies in the direc- 

 tion of the turned orthogonal on the template (Figure 2-20 bottom) ; 



(d) Place a triangle along the base of the template and construct 

 a perpendicular to it so that the intersection of the perpendicular with 

 the incoming orthogonal is midway between the two contours when the dis- 

 tances are measured along the incoming orthogonal and the perpendicular 

 (See Point B in Figure 2-20 bottom) . Note that this point is not neces- 

 sarily on the midcontour line. This line represents the turned orthogonal; 



(e) Repeat the above steps for successive contour intervals . 



If the orthogonal is being constructed from shallow to deep water, the 

 same procedure may be used, except that C2/C]^ values are used instead of 



A template suitable for attachment to a drafting machine can be made. 

 Palmer (1957) , and may make the procedure simpler if many diagrams are to 

 be used. 



2.323 Procedure when a is Greater than 80 Degrees - The R/J Method . In 

 any depth, when a becomes greater than 80 degrees, 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 indi- 

 vidual subintervals, orthogonal-angle turnings are made. 



Referring to Figure 2-21, the interval to be crossed is divided into 

 segments or boxes by transverse lines. The spacing R, of the transverse 

 lines is arbitrarily set as a ratio of the distance J, between the con- 

 tours. For the complete interval to be crossed, C2/C1 is computed or 

 found from Table C-4 of Appendix C. (C2/C^, not 0.-^/^2-^ 



On the template (Figure 2-18), a graph showing orthogonal angle 

 turnings Aa, is plotted as a function of the C2/C1 value for various 

 values of the ratio R/J. The Aa value is the angle turned by the in- 

 coming 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 interpo- 

 lated contour becomes smaller than 80 degrees. At this point, this method 

 of orthogonal construction must be stopped, and the preceding technique 

 for a smaller than 80 degrees used, otherwise errors will result. 



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

 sheltering land forms shield a stretch of shore from waves approaching in 

 certain directions, to construct refraction diagrams from shallow water 



2-73 



