ECHOES OF BATS AND MEN 



ynx, ears, auditory portions of the brain, and the other 

 parts used directly for echolocation. For both bat and 

 radar the power is the peak level reached during each 

 pulse. It may be recalled from Chapter 2 that the ears of 

 bats and men operate at sound power levels ranging from 

 about 10"^^ to 10"* watt per square centimeter. The air- 

 borne radar detection of another airplane at 50 miles is 

 compared with two cases of echolocation by bats— the 

 detection of a 1 -centimeter insect (or pebble) by a big 

 brown bat at 2 meters, and the echolocation of a 0.18- 

 millimeter wire by a Uttle brown bat at 90 centimeters. 

 The j5rst approach to defining the efficiency index 

 might be simply to have R, the distance of detection, 

 in the numerator, and the other three quantities, P 

 (power), W (weight), and d (target size), in the de- 

 nominator, where large values will tend to lower the in- 

 dex. This index, R/PWd, is listed in the next row of the 

 table, and when judged on this basis, the bats appear bil- 

 lions of times better than the radar system. But a little 

 reflection shows that, in defining the index in this way, 

 we have made an important assumption; namely, that 

 these four quantities are really related to one another as 

 we have entered them in the equation. For example, 

 this definition of efficiency assumes that range will in- 

 crease in direct proportion to power. But for all radar 

 systems, and probably all bats, the emitted energy falls 

 off as the square of the distance. And most small targets 

 send back echoes that also obey the inverse-square law. 

 As pointed out in Chapter 4, where insect-catching bats 

 were compared with the hypothetical case of a bat at- 

 tempting to echolocate fish through the air-water inter- 

 face, the energy in an echo is proportional to 1/R*. 

 This means that to obtain twice the range a system of 

 echolocation will need 2*, or 16 times as much power, 

 and we should therefore change our index to contain R 



124 



