522 



OBSERVATIONS OF WAKE ECHOES 



33.2 EXPERIMENTAL PARAMETERS 



The formulas derived in the preceding section are 

 appUed in later sections to the interpretation of echoes 

 from actual wakes. The theoretical results may also 

 be applied to indicate what type of echo-ranging ex- 

 periment is most suited for fundamental studies of 

 wakes. Certain considerations along this line, espe- 

 cially concerning the choice of transducer directivity, 

 pulse length, and frequency are presented in this 

 section. 



33.2.1 Transducer Directivity 



The mathematical intricacies of the analysis given 

 in Section 33.1 .2 are essentially a consequence of the 

 imperfect directivity of the transducers and the finite 

 range over which the wake is observed. The chief re- 

 sult is a variety of wake indices pertaining to specific 

 experimental situations. Fortunately, the picture is 

 greatly simplified in practice, because of the proper- 

 ties of the transducers customarily employed in echo 

 ranging. 



The numerical differences between the different 

 wake indices, for the same directivity pattern, are 

 quite insignificant in proportion to the accuracy at- 

 tainable in acoustic measurements. As an example, 

 Table 2 gives the wake indices computed from 

 the composite directivity pattern of a particular 

 transducer. 



The integral ^ taken over the composite directivity 

 pattern alone, as defined by equation (43), is given 

 for comparison. It would seem that ^ = J, -|- 8 db 



for the other wake indices, if the correction factor sec 

 /3 is applied for oblique incidence of sound on semi- 

 transparent wakes. 



Since the wake index *' applying to short-pulse 

 echoes depends on the range and on the attenuation 

 coefficient inside the wake, Table 2 gives a more de- 

 tailed illustration of the influence of the variable 

 parameters. The effect is seen to be quite small; there- 

 fore it does not influence the interpretation of the 

 experiments on the E. W. Scripps wake carried out 

 on November 28, 1944, during which the two trans- 

 ducers referred to in Table 3 were employed. 



As far as the range is concerned, there is a distinc- 

 tion between short and long pulses. In order to obtain 

 short-pulse echoes of a kind that can be treated by a 

 simple acoustic theory, the sound beam must be 

 trained perpendicularly at the wake and the range 

 must be shorter than 200 times the signal length; 

 equation (35) of Section 33.1.2, which formulates 

 this condition in an exact manner, shows that the 

 exact factor is a function of the directivity pattern 

 of the transducer. Short-pulse echoes produced mth 

 a sound beam trained obUquely at the wake defy 

 any simple mathematical analysis and, therefore, are 

 of little use in the study of wakes. As regards long- 

 pulse echoes, however, the range is of minor im- 

 portance, and the aspect of the wake is of no conse- 

 quence whatever because the dependence of the wake 

 index on the aspect angle /3 is fully taken into account 

 by equations (40) and (41). In practice, it should 

 suffice to keep the ratio of wake width w to range r 

 less than about 0. 1 ; this value of w/r makes it possible 

 to neglect the inverse-cube correction factor appear- 

 ing in equation (15),- which was omitted from there on. 



may be used in place of any of the rigorous values of 

 the wake indices, except for *^o with obliquely imping- 

 ing sound beam (/3 = 60 degrees). In this particular 

 case the wake index includes the factor sec /?, as is 

 physically evident for reflection from a semi-trans- 

 parent layer of finite thickness. It is concluded, then, 

 that for all practical purposes ^ may be substituted 



33.2.2 



Pulse Length 



Pulses varying in length from 0.3 to several hun- 

 dred milliseconds have been employed in echo rang- 

 ing at wakes. There are some general considerations 

 concerning signal length that apply primarily to the 

 tactical use of wake echoes. In practice, the design 

 of the keying circuits and the build-up time of the 

 transducer set a lower limit to the pulse length. While 

 so far no special study has been made of the optimum 

 conditions for recognition of wake echoes, it may be 

 surmised, from experience with echoes from finite 

 targets,^ that signals shorter than 10 msec are not 

 suitable for satisfactory recognition by ear. But wake 

 echoes obtained with 1-msec signals, and even with 

 shorter ones, are readily recognized on sound range 



