66 TECHNICAL SURVEY 
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 
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 
For example, 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 
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 107% 
unit per 1,000 ft, while at 15,000 ft it is only 6 X 107% 
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. 
Separation Standard Tropical Tropical 
of planes atmosphere atmosphere dry 
(feet) (feet) (feet) (feet) 
Range.50 miles 
5,000 35 24 317 
10,000 73 107 380 
20,000 131 243 514 
30,000 171 306 572 
Range 75 miles 
5,000 78 54 713 
10,000 164 242 924° 
20,000 287 539 1,158 
30,000 389 693 1,290 
Range 100 miles 
5,000 139 97 1,270 
10,600 376 431 1,644 
20,000 527 960 2,061 
30,000 673 1,237 2,296 
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. 
RANGE 
Errors in range due to vertical refraction within 
a duct are approximately of the order of 1 yd in 
50,000 yd. The error in range corresponding to an 
azimuth error of 0.05° is estimated at less than 0.2 
yd in 50,000 yd. 
AZIMUTH 
Errors in azimuth arise from horizontal! variations 
in the index of refraction in the atmosphere. Generally 
these variations are of insufficient magnitude to :cause 
such errors to be appreciable. In order to obtain an 
error of 0.05° in 50,000 yd it can be shown that a 
change in the index of refraction of 1.5 X 10° unit 
in 44 yd perpendicular to the path of propagation 
is required. This corresponds to an increase of 1C 
temperature and a decrease of 0.1 mb in vapor 
pressure. Such changes within 44 yd may occur in 
propagation parallel to a sea coast or to a sharp 
cold front, or in isolated regions such as between 
forest and meadow, valley and plain, or land and 
water surfaces. Except in the vicinity of a cold front 
or sea coast it is unlikely that such horizontal gradi- 
ents of the index of refraction exist along the entire 
path of the ray. 
CONCLUSIONS 
1. For gunlaying (antiaircraft) radar, the maxi- 
mum error in angle of elevation at 29,000-yd range 
is 0.9 mil, as compared to a military tolerance of 
1.5 mil. 
2. In early warning heightfinding radar, errors of 
1,000 ft absolute altitude at 75 miles range may be 
exceeded even with the application of a standard 
atmosphere (% earth radius) correction. Because of 
ducts, errors may be as much as 2,000 ft at 50 miles. 
Errors in relative altitude may likewise exceed 500 
ft in 75 miles. 
3. Errors in azimuth may exceed 0.05° in 50,000 
yd in propagation parallel to a sea coast or a cold 
