372 REFRACTION AND REFRACTIVE INDEX MODELS 



8.4.9. Height Error Equations 



The equations for approximating e^ were determined as 



eh, = aio jrj + -B~ 9i + k, (8.52) 



D D"^ 



eh, = a2o -7-7 + -jB" ^2 + k, (8.53) 



and 



en, = 030 7— H — ^ (?3 + A; (8.54) 



where 



D = R'' - 0.03587 /i^'. 



Values for gi from (8.46) through (8.48) are found from 



fiiiha) = a,i + a^-Jia + a,3/ia^ , («' = 1, 2, 3) , (8.55) 



/i2(/ia) = an + a,5/ia , (z = 2, 3) , (8.56) 



and 



fzzQia) = age + a^^ha (8.57) 



for R in miles and /la in thousands of feet. The term in D/h^ was intro- 

 duced to account for, in part, a large negative constant term which tended 

 to produce negative height errors for ranges less than 30 mi. Further- 

 more, the inclusion of this term increased the accuracy of the estimate of 

 thi by about 2 percent. An additional term in hj' for (8.55) increased 

 in the accuracy by about 1 percent but introduced a fictitious minimum 

 near 60,000 ft, while a term in ha~ for (8.56) and (8.57) increased the 

 accuracy of (8.53 and (8.54) by less than 0.1 percent. The relative im- 

 provement of (8.53) over (8.52) is about one percent. The coefficients 

 aij are listed in table 8.8. The constant term, k, which would vanish 

 if the equations were exact, is about —70 for a least squares approxima- 

 tion. 



