108 



RADAR ERRORS DUE TO ATMOSPHERIC REFRACTION 



Table 2. Errors in absolute altitude for early warning 

 heightfinding. Range 75 miles. 



True Angle of sight (degrees) Errors in altitude (feet) 

 angle Standard Tropical Standard Tropical 



Ducts in the lower layer of the atmosphere will 

 cause errors to exceed those specified by military 

 characteristics. For a duct depth of 25 ft and 1-unit 

 decrease in the modified index of refraction, errors 

 in absolute altitude may exceed 1,000 ft within 

 ranges of 50 miles. A 200-ft duct, in which the 

 modified index of refraction decreases 10 units, may 

 cause an error of more than 2,000 ft in 50 miles 

 range. Figure 2 depicts errors in absolute altitude 



levels. Even in a standard atmosphere errors in 

 relative altitude arise since the rate of decrease of 

 the index of refraction near sea level is 12 X 10 -6 

 unit per 1,000 ft, while at 15,000 ft it is only 6 X 10 -6 

 unit per 1,000 ft. In a tropical atmosphere with dry 

 air aloft the errors are likely to be considerably 

 greater since the rate of decrease of the index of 

 refraction with height is greater. 



Table 3. Errors in altitude relative to lowest plane 

 located at 3,000 ft above mean sea level. 



50 75 



RANGE IN MILES 



Figure 2. Maximum errors in absolute altitude due to 

 surface ducts with standard atmosphere above. 



for ducts of various depths on the assumption that 

 the ray just escapes the top of the duct into a stand- 

 ard atmosphere above. The rate of decrease of the 

 modified index of refraction in the duct is 1 unit 

 per 20 ft (corresponding to a curvature of the ray 

 about twice that of the earth). 



Relative Altitude 



As an exmple, let us assume that five aircraft are 

 located at altitudes of 3,000, 8,000, 13,000, 23,000, 

 and 33,000 ft above mean sea level. Suppose that 

 these planes are detected by radar at ranges of 50, 

 75, and 100 miles. Errors in relative altitude occur 

 because of differential refraction at high and low 



Thus in a tropical atmosphere with dry air aloft 

 such as exists in the trade wind areas over the ocean 

 errors of some 500 ft relative altitude for planes 

 separated by 20,000 ft would occur in a range of 50 

 miles. For 100-mile range, errors can be as much as 

 2,000 ft. Even in a standard atmosphere errors are 

 more than 500 ft for ranges of 100 miles for the 

 higher level planes. 



Azimuth and Range 



Errors in azimuth are negligible for all meteoro- 

 logical conditions except possibly for propagation 

 parallel to a sea coast or sharp cold front (see para- 

 graph below). Errors in range are likewise negligible 

 for all possible meteorological conditions. 



Surface Surveillance Radar 



Military characteristics for sets AN/MPG-1 and 

 AN/FPG-2 specify errors up to 0.05° in azimuth at 

 28,000 yd and 50,000 yd respectively. Range error 

 toleration is 20 yd in 50,000 yd. 



