SONAR AND RADAR 



to the fourth power instead of the first. This will greatly 

 increase the rating scored by the radar set detecting an 

 airplane at 50 miles. 



Having made this improvement in the index, we 

 should also scrutinize the other variables in our equa- 

 tion, in particular the size of the target, d. If a series of 

 targets is fairly large relative to the wave length of the 

 signal being used to generate an echo, the echo power is 

 usually proportional roughly to their areas, or to d^. 

 This is true of most radar targets, and certainly of air- 

 planes being echolocated with 3.2-centimeter waves. Is 

 it also true for bats? The insects they catch vary from 

 somewhat below one wave length to several wave 

 lengths, and of course the FM bats employ orientation 

 sounds containing a whole octave of frequencies, or a 

 twofold range of wave lengths in each pulse. It is prob- 

 ably reasonable to assume that in insect detection the 

 echo power varies as the square of the target diameter, 

 although in some cases the insects may be enough below 

 one wave length so that this assumption would lead to 

 an overestimate of the echo strength. The next line of the 

 table therefore lists for each of the three systems the 

 value of the revised efi&ciency index, R^/PWd^. Even 

 on this basis the bats are somewhat superior to the radar. 



Finally, we should pay a little more attention to the 

 bats which detect wires far smaller than one wave length, 

 such as the little brown bat listed in the third row of 

 the table. When wires or other cylindrical obstacles are 

 much smaller than one wave length, the echo power var- 

 ies as d^, and the 0.1 8 -millimeter wires detected at 90 

 centimeters are certainly in this size range. This domain 

 of target size produces what is sometimes called Rayleigh 

 scattering, after the nineteenth-century physicist who 

 analyzed it with special reference to Ught scattered by 

 tiny particles in the air. Such light makes up most of 



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