higher values of ALy/^^^ o The method for their use is the same as that 

 for the scale devised by 'Johnson et al for drawing orthogonals shoreward 

 from deep water, except that the direction of turning is reversed. Figure 

 U demonstrates the method of use. 



The use of equation (2) is limited to values of a, les& than about 

 7O-75O5 since, as a, + Ja approaches 90°, tan {a, -h Aa ) becomes infinite^ 

 resulting in very rapid changes In AOC o This necessitates the crossing of 

 a contour interval in a series of short steps, and it is therefore desirable 

 to employ equation (1) whenever Or, exceeds about 75° « For values of CC^ 

 greater than 75° , sin( (X. i-ACK ) may be given the value of 1, and the equa- 

 tion becomes 



or the same as used in bringing orthogonals into shore from ddep water at 

 high values of CX » Hence, at large values of OC, , when it is necessary 

 to use the r/J method, the protractor developed by Johnson, O'Brien and 

 Isaacs should be used. The method is again the same, me re ly^ reversing the 

 direction of curvature of the orthogonals. 



Figure 5 shows a comparison of an orthogonal drawn from shore out with 

 one drawn from deep water into shore „ 



Acknowledgment 



Much of the computing necessary for the development of these protractors 

 was done by Fo Re Lewis, now with the Uo So Navy„ 



REFERENCES 



(1) Dunham, J„ Wo - Refraction and diffraction diagrams a Unpublished 



paper given at Institute of Coastal Engineering, 12 October 1950.. 



(2) Johnson, Jo Wo, Mo Po O'Brien, and Jo D. IsaacSo - Graphical con- 



struction of wave refraction diagrams,, U, S, Hydro graphic Office 

 Technical Report No, 2, H. 0, Pub, No, 605;, January I948. 



