USE OF EFFECTIVE EARTH'S RADIUS 361 



target position and the refractive index structure, (8.36) will provide a 

 simple formula for approximating the height error, 



since for target heights (h < 70,000 ft) at the maximum range (R c^ 150 

 mi) to be considered 



I ^ - -^ I < 20 ft, 



Ve 2re 



or less than one percent of the total height error. 



If the curvature of a ray, 1/p, at any point on the path is called K, then, 

 from (8.29) and (3.20) 



_ Wo cos 00 dn 

 ^ ~ 71^(1 + h/ro) dK ^^-^^^ 



From (8.32) ignoring terms of the order l/r^f, one obtains 



so that (8.38) becomes 



J. no {R" - hiy " V "^ Vo) dn_ (8.40) 



~ n' R / , \ dh ' 



To/ 



1 + 



ro 

 The refractive index usually decreases with height so that the quantity 



1/2 



(-6" 



no ^ . 



n2 1 + ^ — ^ 



To 



varies only slightly with height, and the curvature at a point on the ray 

 path can be approximated by 



i^r 



K^('-^^)"'\'i\. (8.41) 



