THEORY 335 



Such a plot is shown in figure 8.16 for a small initial elevation angle, 

 50 mrad (about 3°), and a "target" height beyond the atmosphere, 70 km. 

 The family of A^ profiles used in ray tracing this sample of bending values 

 is referred to as the CRPL Standard Sample. ^ It can be seen from inspec- 

 tion of figure 8.16 that the assumption of linearity expressed in (8.18) is 

 justified for this case. A similar conclusion can be reached from examina- 

 tion of data for other cases, including low target heights and elevation 

 angles down to zero degrees, although for these extremes the degree of 

 correlation between t and N s is not as marked as that shown in figure 8.16. 

 The other refraction variable treated in this section is the radio range 

 error, ARe, which is here defined as being that error incurred in measuring 

 the distance between two points by means of timing the transit of radio 

 signals between the points, and assuming that the velocity of propagation 

 is equal to that of free space. For the case of a radio ray, this error is 

 composed of two parts: the difference between the curved length of the ray 

 path, called the geometric range, Rg, and the true slant range, Ro; and 

 the discrepancy caused by the lowered velocity of propagation in a refrac- 

 tive medium. The geometric range is given by 



Rg = / CSC 6 dh, 







and the apparent, or radio, range by 



J n 



Jo 



Thus the total radio range error, ARe — Re — Ro, is given by 



fht 



ARe = I n CSC 6 dh — Ro, 



Jo 



Re ^ I n esc d dh. 



or 



ARe ^ 10 ^ f N CSC ddh -\- I esc d dh - Ro. ,^ ,^. 



Jo (o.iyj 



^Meaning explained in section 8.3.3. 



