SCHULKIN'S METHOD 55 



heights; one then assigns to N(h) a Hnear variation with height in between 

 the tabulated profile points, so that the resulting A^ versus height profile 

 is that of a series of interconnected linear segments. Under this assump- 

 tion, (3.2) is integrable over each separate linear A'^-segment of the profile 

 (after dropping the n term in the denominator, which can result in an 

 error of no more than 0.04 percent in the result), yielding the following 

 result : 



An.2(rad) ^ - f"'"' cot d dn ^ '^^'^' ~ ""'^ 



tan di + tan 62 ' 

 or 



ATi.2(mrad) ^ — „ . . — . (3.11) 



tan 0] + tan d-i 



For the conditions stated above, this result is accurate to within 0.04 

 percent or better of the true value of An, 2, an accuracy that is usually 

 better than necessary. Thus it is possible to simplify (3.11) further by 

 substituting 6 for tan 6; this introduces an additional error that is less than 

 1 percent if 6 is under 10° (^^175 mrad). Now (3.11) becomes 



2 (A/", — N'>) 

 Ari,2(mrad) ^ - q^ j^ q^ , (3-12) 



(mrad) (mrad) 



where 6 may be determined from (3.58). 



The bending for the whole profile can now be obtained by summing 

 up the An, 2 for each pair of profile levels: 



r.(mrad) S t ^ ^f "f"^'' . (3.13) 



(mrad) (mrad) 



This is Schulkin's result. The degi'ee of approximation of (3.13) is 

 quite high, and thus most recent "improved" methods of calculating r will 

 reduce to Schulkin's result for the accuracy obtainable from RAOB or 

 other similar data. Thus, provided that the A'^-profile is known, (3.13) is 

 the most useful form for computing bending (for all practical purposes) 

 that should concern the communications or radar engineer. Some other 

 methods have been published which are actually the same as Schulkin's, 

 but have some additional desirable features; e.g., the method of Anderson 

 [7] employs a graphical approach to avoid the extraction of s(iuare roots 

 to obtain 0^. 



