KANGE DEPENDENCE 



429 



200 250 300 



350 400 450 500 550 600 

 RANGE IN YARDS 



Figure 10. Range dependence at off-beam aspects for 

 moving vessels (New York). 



ranges; (2) reduced reflection as the range approaches 

 the dimensions of the target; and (3) incorrect evalu- 

 ation of the transmission loss. The first effect applies 

 only to the measurements on moving vessels at San 

 Diego, since the somid beam used during the New 

 York tests was wide enough to cover the target at all 

 ranges. The second applies primarily to measure- 

 ments on anchored vessels where specular reflection 

 seems most likely to occur, and the third applies to 

 measurements on both moving and still ships. 



Table 3. Range dependence. 



At short ranges, how much of the target the sound 

 beam covers depends on the dimensions and aspect 

 angle of the target and on the directivity pattern of 

 the transducer. At San Diego, a standard JK trans- 

 ducer was employed, which had a total beam width 

 of 20 degrees between points on either side of the 

 axis where the response was 10 db lower. If it is 

 assumed that the sound beam was 20 degrees wide 

 and that the destroyer was 300 ft long, then the 

 sound beam did not cover the ship, at beam aspect, 

 at ranges less than about 300 yd. Since many of the 

 beam target strengths were measured at shorter 

 ranges, this failure of the sound beam to cover the 

 sliip may account for the decrease in target strength 

 with decreasing range. 



24.4.1 Transducer Directivity 



To evaluate the effect of the transducer directivity 

 on the target strength-range dependence, the differ- 

 ence between the echo level from a destroyer at beam 

 aspect and from a small target always within the 

 sound beam was calculated, as a function of range, 

 from the directivity pattern of the transducer. This 

 difference is expressed as 



10 



log r 



Jo 



¥i<t>)dx 



(^2 _|. ^2)2 



10 log 



Xi 



(1) 



where Xi is the length of the target in a direction per- 

 pendicular to the sound beam; 6^(<^) is the composite 

 directivity pattern of the transducer; and r the range 

 to the center of the target. This difference in decibels 

 between the echo level from the destroyer and the 

 echo level from a small target of the same target 

 strength, as the range is decreased from 650 to 100 

 yd, is superimposed on Figure 7 as a broken line. The 

 zero level, where the sound beam effectively covers 

 the entire target and the two echo levels are the 

 same, is placed at a target strength of 23.5 db, which 

 is the average beam target strength measured at San 

 Diego at ranges of 450 yd and greater. The difference 

 calculated from equation (1) amounts to about 7 db 

 at a range of 100 yd, and drops to less than 1 db at 

 ranges greater than 500 yd. 



This analysis does not take into account the ex- 

 tension of the target by the wake. However, even if 

 the target were assumed to extend infinitely in one 

 direction, the target strength for long pulses would 

 increase only as 10 log r and would not be signifi- 

 cantly different from the broken curve in Figure 7. 

 The increase of target strength with range in such a 

 case would be analogous to the similar increase for 

 the target strength of wakes discussed in Section 

 33. 1 . 1. This failure of the soimd beam to cover the en- 

 tire target, especiallyat short ranges, is responsible for 

 much of the dependence of target strength on range 

 observed at San Diego at beam aspect. Apparently, 

 however, it is not responsible for all the dependence 

 observed. 



Significantly, these echoes from destroyers at beam 

 aspect are approximately as strong as echoes ob- 

 served from the wakes directly behind the destroy- 

 ers. In Section 24.1 it was noted that echo-ranging 

 experiments were made on the wakes after the de- 

 stroyers passed; in these measurements, the sound 

 beam was perpendicular to the axis of the wake. 

 The wake echoes showed the same variation with 



