EFFECTS OF REFRACTION 



313 



15 



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10 20 30 40 50 60 70 80 



PERCENT GREATER THAN INDICATED VALUE 



Figure 6. Cumulative distribution of observed ratio: 



Range to reverberation peak 

 Water depth 



90 



95 



98 99 



may be defined as water in which the temperature 

 at the bottom differs from the temperature at the 

 surface by less than five degrees. 



Actually, examination of the data in reference 1 

 shows that relatively few of the reverberation curves 

 analyzed were obtained in isothermal or nearly iso- 

 thermal water. Thus, the results of that study do not 

 apply to water in which the top-to-bottom tempera- 

 ture change is less than five degrees. This fact helps 

 to account for the disparity between the observed 

 range of the reverberation peak, characteristically 

 about six times the depth, and the predicted value 

 of 10 to 12 times the depth for isothermal water. 



After these preliminary remarks, we may examine 

 the San Diego results in more detail. Figure 6 is a 

 cumulative plot, taken from reference 1, of the ratio 

 of the range of the bottom reverberation peak to the 

 water depth. The median point on this curve cor- 

 responds to a range-depth ratio of 6.2. Fifty per cent 

 of all peak ranges were found to lie between 5.1 and 

 7.2 times the depth, and 80 per cent to lie between 

 4 and 8 times the depth. These results agree well 

 enough with the results of another study by UCDWR.^ 

 In reference 2, which, however, was based on a 

 smaller number of reverberation curves, the average 

 range to the peak was about 5 times the depth. The 

 difference between these two estimates of the ratio 

 of the range of the peak to the water depth is prob- 

 ably due to sampling and to the fact that the rever- 

 beration curves plot only a few isolated points of the 

 measured film. The data discussed in reference 2 are 

 described in somewhat more detail in Section 15.3.1; 



they were obtained by using a transducer whose 

 beam pattern was similar to that of standard Navy 

 echo-ranging gear. Bathythermograph data and ray 

 diagrams were available, and it was found that the 

 range to the reverberation peak corresponded to 

 about the range where the 6-degree ray reached the 

 bottom. In another internal report by UCDWR,^ it 

 was found that the range of the peak usually cor- 

 responded to the range at which the 5-degree ray 

 reached the bottom. 



For standard Navy gear at 24 kc, the half beam 

 width y defined in Figure 4 of Chapter 12 is close to 

 6 degrees. Thus, the results described in the preceding 

 paragraph suggest that with standard gear at 24 kc 

 the range where the beam's edge (5- or 6-degree ray) 

 strikes the bottom is the range of the reverberation 

 peak. These results suggest furthermore that in water 

 which is not "nearly isothermal" the range of the 

 reverberation peak is between four and eight times 

 the depth. For simple temperature gradients, it is 

 easy to estimate the range at which various rays 

 will strike the bottom, as a function of the depth to 

 the bottom.* Table 1 gives the results of such calcu- 

 lations, for various initial ray angles, water depths, 

 and surface-to-bottom temperature differences; in 

 computing this table it was assumed that the tem- 

 perature decreased linearly from the surface to the 

 bottom. It is clear from the table that with linear 

 gradients the 6-degree ray always does strike the 

 bottom at a range between 4 and 8 times the water 

 depth, when the temperature difference between the 

 projector and bottom is greater than 5 degrees. 



