DISCUSSION 

 A METHOD FOR DRAFTING ORTHOGONALS SEAWARD FROM SHORE 



The Bulletin is always glad to receive discussion of its articles, 

 and is pleased to present the following discussion of Mr. Saville's 

 article W A Method for Drawing Orthogonals Seaward from Shore 1 * which 

 appeared in the October 1951 issue of the Bulletin. The discussion is 

 by Mr. Kenneth Kaplan of the San Francisco District, Corps of Engineers. 



In 1%9 and 1950 this office was engaged in a general study of 

 possible small -craft harbors on the northern California coast. This 

 study required the drawing of many refraction diagrams, and for conven- 

 ience, many refraction fans. The first attempts at drawing these fans 

 were made merely by reversing Isaac's orthogonal technique 5 that is 

 using for A ex that value determined from the standard nomograph with 

 the calculated Ai/L av value and a value for angle designated by the 

 author as <x' „ This method, quite naturally, was found to be highly 

 inaccurate for any situation in which the Act was relatively large. 



Accordingly, Mr. R. W„ Lowe, formerly of this office, developed, 

 in late 1949 » a method which essentially consists of taking the first 

 approximation of a successive approximation series for the determination 

 of Aoc „ The angle between the level line between contours and the 

 normal to a seaward projected orthogonal is measured (call it ex' ) and 

 a value (say) Act' is determined from Isaac's nomograph with this and 

 the correct AL/L A y value. These two values a'4Aa'are added to find 

 the approximate value of ex , which in turn is used to find the ap- 

 proximately correct Ace . The method is simple, requires the use of 

 no protractors (the drafting machine's two arms are ideal), and permits 

 the drawing of orthogpnals well within the accuracy desired. 



The method the author presents is, of course, a refinement of the 

 above but, since it makes necessary the use of additional protractors, 

 I believe the refinement introduced is unwarranted. For the construction 

 of a fan diagram either method will give approximately the same results, 

 and the simpler one is to be preferred. In addition, an orthogonal 

 constructed by use of either method cannot safely be used as a true 

 orthogonal but merely as an indication of the correct deep-water position 

 and direction of approach. 



This last statement needs some amplification. A level line between 

 two contours is established by averaging the angles between a projected 

 orthogonal and the two contours. (See Johnson, O'Brien and Isaacs, H. 0. 

 Publication No. 605, page 26, step 6). Reference to the following 

 figure shows that a level line so determined with a shoreward projected 

 orthogonal may well differ from one determined with a seaward projected 



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