TRANSMISSION LOSS 



373 



standard deviation of 8.5 db when an attenuation 

 coefficient of 20 db per kyd was assumed; when the 

 transmission loss measured aboard tiic suijmaiinc 

 was used in tlie computations, the beam-target 

 strength rose to 40 db with a much smaller standard 

 deviation of 3.5 db. In most trials reported here, it 

 was necessary to e\'aluate the transmission loss from 

 an attenuation coefficient, estimated for each run from 

 the echo-ranging frequency employed and sometimes 

 from the prevailing oceanographic conditions. 



21. .5. 3 Estimating the Attenuation 

 Coefficient 



The attenuation coefficient in sea water varies 

 widely and depends primarily on the frequency of the 

 echo-ranging sound and on the prevailing oceano- 

 graphic conditions.'^ For example, in mixed water, or 

 water of constant temperature, at least 50 ft deep, 

 this coefficient is about 5 db per kyd at 24 kc, and in 

 the neighborhood of 15 db per kyd at 60 kc. A plot of 

 the attenuation coefficient against frequency for 

 ideal sound conditions is reproduced in Figure 7 and 

 represents a rough average of observations primarily 

 at 20, 24, 40, and 60 kc; the increase in attenuation 

 coefficient with frequency is quite mai'ked and shows 

 why it is impractical to use very high frequencies for 

 echo ranging. 



The attenuation coefficient increases markedly 

 with poor sound conditions. At 24 kc, it may be as 

 high as 15 db per kyd under poor conditions, or even 

 40 db per kyd under extremely bad conditions. 



Very few data are available at 60 kc on the varia- 

 tion of the attenuation coefficient with oceanographic 

 conditions. Empirical formulas have been derived for 

 the attenuation coefficient at 24 kc, however, as a 

 function of the depth of the thermocline. For a hydro- 

 phone above the thermocline, 



170 

 a = 3.5 + — , (5) 



and for a hydrophone below the thermocline 



260 



a = 4.5 -H — , (6) 



where a is the attenuation coefficient in decibels per 

 kiloyard and D is the depth in feet to the thermocline. 

 The probable error is about 2 db per kyd.'^ As implied 

 in Chapter 5, these empirical formulas are, in general, 

 less suitable for predicting the attenuation coefficient 

 than other methods based on a more quantitative 



classification of the variation of temperature with 

 depth, becau.se tran.smi.ssion anomaly-range graphs 

 significantly depart from straight lines under certain 

 conditions. However, equations (5) and (6) are suf- 

 ficiently accurate for the present purposes. 



Early target strength measurements showed that 

 different values of the transm.ission loss were obtained 

 by different methods, as described in Section 21.5.2. 

 Therefore, in most calculations representative values 

 of 5 and 20 db per kyd at 24 and 60 kc respectively 

 were taken for the attenuation coefficient. Much of 

 the time no account was taken of the oceanographic 

 conditions which prevailed at the time of the tests, 

 however, with the result that the reported target 

 strengths varied considerably. Examples of this varia- 

 bility are given in Section 21.6 of this chapter. 



2]. 5. 4 



Surface Reflections 



Reflection of sound from the surface of the ocean 

 is neglected in all calculations of target strengths. 

 Such an effect would offset, in part, the loss in in- 

 tensity caused by spreading and absorption. 



Perfect specular reflection from the surface would 

 effectively double the intensity of the sound incident 

 on the target and the intensity of the echo returned 

 to the projector, under ideal conditions. In other 

 words, it would reduce the transmission loss by 3 db 

 each way, or by a total of 6 db from the projector to 

 the target and back again. Thus, in equation (4) the 

 constant b would equal —3 db at ranges of a few 

 hundred yards or more. 



Some evidences of surface reflection have been 

 found experimentally. At San Diego a number of 

 o.scillograms of echoes from submarines have shown 

 peaks or "spines" at the beginning and end of each 

 echo, separated by a relatively smooth echo of lower 

 intensity; an example is shown in Figure 8 for an 

 S-boat at beam aspect." The first peak is attributed 

 to direct reflection from the hull of the submarine 

 alone when the first part of the pulse strikes the tar- 

 get and is reflected back to the projector along the 

 shortest possible path; the final peak comes from the 

 ray reflected from the submarine to the surface and 

 back to the projector, after the direct echo from the 

 submarine has been received. In other words, the two 

 spines are attributable to reflection along only one 

 path, since there will be a short time at both the 

 beginning and end of the echo when the sound travels 

 only one path back to the transducer. The intensity 

 of the intervening echo is consequently lower because 



