Chapter 19 

 PRINCIPLES 



WHEN A TARGET is in the path of a sound beam, 

 the intensity of the reflected sound measured 

 some distance away will, in general, depend on many 

 factors, such as the intensity of the sound striking 

 the target, the distance from the target to the point 

 where the echo is measured, and the size, shape, and 

 orientation of the target. Often it is desirable to 

 separate these different factors so that the effects of 

 the size, shape, and orientation of the target may be 

 discussed independently of all other factors. 



Such a separation is possible only when the radii 

 of curvature of the sound waves striking the target 

 and returned to the receiver are both much larger 

 than the dimensions of the target, in other words, 

 when the waves incident on the target and the waves 

 reflected back to the receiver are essentially plane. In 

 terms of ray acoustics, the incident sound rays must 

 be substantially parallel over the area of the target 

 which they strike, and the reflected sound rays 

 must be parallel over the area of the face of the re- 

 ceiver. 



In this chapter target strength is defined quanti- 

 tatively in terms of the echo level, the source level, 

 and the transmission loss. Then the target strength 

 of a sphere is derived as a function of its radius. 

 Finally, the effect of pulse length on target strength 

 is examined for a simple case. Ray acoustics is em- 

 ployed throughout the chapter, and the arguments 

 are necessarily idealized. No account is taken of the 

 wave character of sound; in other words, all effects 

 attributable to the wave nature of sound such as in- 

 terference, diffraction, and phase differences are ex- 

 plicitly ignored. The conditions under which this ap- 

 proximation is valid are discussed in Section 19.4. A 

 more detailed theory of target strength in terms of 

 wave acoustics is presented in Chapter 20. 



19.1 DEFINITION OF TARGET STRENGTH 



Let /o be the intensity of the incident sound strik- 

 ing a stationary target, and Ir the intensity of the re- 

 flected sound measured at some particular point. If 



If, is doubled, Ir will also be doubled, other factors 

 remaining unchanged; that is, the intensity of the 

 reflected sound will be directly proportional to the 

 intensity of the incident sound. 



For a given value of /o, Ir will depend on the 

 orientation of the target relative to the incident 

 sound and also on where the echo is measured. This 

 dependence of h may be quite complicated. In practi- 

 cal echo ranging, however, the problem is simplified 

 because the echo is always measured back at the 

 source — in other words, it is always measured in the 

 same direction as the projected sound, and the target 

 strength depends only on the orientation of the target. 

 Therefore, it will be assumed throughout this chapter 

 that the echo is measured at the source. Although this 

 admittedly is not the most general case, it is the only 

 case of practical importance for echo ranging. 



19.1.1 Inverse Square Transmission 

 Loss 



The dependence on distance, although complicated 

 near the target, becomes very simple far away from 

 the target, if the sound rays are assumed to travel in 

 straight paths in an ideal medium, with boundaries so 

 far away that their effects on sound propagation can 

 be neglected. It has been shown in Section 2.4.2 that 

 the intensity of sound from a point source, in this 

 ideal case, falls off inversely as the square of the 

 distance from the source. This same inverse square 

 law applies to sound reflected from any target at 

 distances much larger than the dimensions of the 

 target, since at such distances the target behaves as 

 a point source of sound. 



Why the inverse square law holds for the intensity 

 of sound reflected from any target, at large but not at 

 small distances, may best be understood by studying 

 Figure 1. Here are shown rays reflected from a target, 

 A to a point near the target, and B to a point far 

 away from the target. Rays reaching a point near the 

 target come from different points on the target and 

 from various directions, if the surface is irregular. 



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