766 AIRBORNE NAVIGATION AND GROUND SURVEILLANCE 



where R^cpd = illuminated area at range R for an antenna of half power 

 beamwidths of </> and d 



T = pulse length 



c = velocity of propagation of light 



n = scattering cross section per unit volume of target (Equation 

 14-14). 



If attenuation due to intervening media 7 is now given as the summation 

 of attenuations of i number of individual cells of path lengths L,-, Equation 

 14-18 may be rewritten^": 



Several important conclusions can be drawn from this equation. First, 

 reflected power varies directly with pulse length r. This derives from the 

 purely incoherent nature of the replies from weather scatterers. Total 

 return energy will continue to increase for a period equal to r as back- 

 scattering from within the target reinforces that from the leading edge. 

 Also, as target size approaches or exceeds that of the illuminated area 

 (a beam-filling target) the R~ term in the numerator reduces the equation 

 for received power to an inverse function of the square of the range rather 

 than the fourth power of range usually associated with radar targets. Thus 

 we see that the designer does have some control over a in Equation 14-20, 

 through the relation of frequency and antenna size to beamwidths and 

 through control of pulse width r. 



14-13 RELATIVE IMPORTANCE OF DESIGN VARIABLES 

 IN AIRBORNE WEATHER RADAR 



Frequency. This factor is considered first because it figures in so 

 many facets of the problem. Antenna gain G varies inversely with X^; beam- 

 widths become narrower with increased frequency; and back-scattering n 

 increases as a fourth power of frequency. Likewise, losses caused by 

 attenuating media are highly frequency-sensitive (note Fig. 14-14). The 

 designer must also consider the size and weight increase of RF components 

 at lower frequencies. Because optimizing each of these factors is not 

 mutually compatible, the choice of frequency of necessity becomes a 

 compromise. As a result, most air-weather radars today operate at either 

 C or X band (usually 5400 Mc and 9375 Mc respectively). 



loj. C. Johnson, Meteorological Factors and Their Effects on Microwave Propagation, Tech- 

 nical Memorandum 412, Hughes Aircraft Co., 1955. 



