4-18] REFRACTION EFFECTS IN THE ATMOSPHERE 233 



Andrew, Axford, and Sugden^^ measured the attenuation at X band in 

 the flame of a rifle flash. They found values in the brightest part of the flash 

 of 0.6 db /cm. 



The results quoted show that the attenuation in the flames of propellant 

 gases can be serious whenever the geometry is such that the flame is a large 

 obstacle in the path between transmitter and receiver. For example, a flame 

 length of 1 meter in the path could introduce an attenuation at X band in 

 the order of 50-60 db. The eff"ects of the flame are likely to be most serious 

 as the missile ascends into rarefied air and the size of the flame grows. This 

 indicates that special thought should be given to the location and design of 

 the antenna on the missile in order to avoid placing the flame directly in the 

 propagation path. 



4-18 REFRACTION EFFECTS IN THE ATMOSPHERE 



In computing the power received from a target by means of the radar 

 Equation 4-1, allowance was made for a process other than free-space 

 propagation by means of the propagation factor F. A process which can 

 produce profound modifications is refraction in the atmosphere. 



The atmosphere is a nonhomogeneous dielectric because of the variation 

 of its pressure, temperature, and humidity. The variations actually are 

 three-dimensional, but the most pronounced refraction eflfects are caused 

 by variations in a vertical direction. 



In a homogeneous atmosphere, it is convenient to plot rays as straight 

 lines and to show the earth's surface (assumed to be smooth) as a curve. 

 If the atmosphere is not homogeneous it is then more convenient to use the 

 earth's surface as a frame of reference. Rays which are straight lines in 

 space then appear as curves when referred to the earth's surface as the 

 abscissa. This is equivalent to the situation where the earth \s,flat and the 

 (homogeneous) atmosphere has a constant positive gradient of refractive 

 index. This is known as the earth-flattening procedure, in which the actual 

 refractivity of the atmosphere is replaced by a modified refractive index. 

 The modified index is denoted by M and is determined by the equation 



M = {n-\+ hi a) X 10« = A^ + ^^^ (4-82) 



a 



where h = height above the earth 



a = radius of the earth. 



Its unit of measurement is called the M unit. N is called the refractivity, 

 and is the excess of the refractive index over unity, measured in parts per 



*^E. R. Andrew, W. E. Axford, and T. M. Sugden, "The Measurement of Ionization in a 

 Transient Flame, Trans. Faraday Soc. A4t, ^HA31 (1948). 



