BEAM ECHOES FROM SUBMERGED SUBMARINES 



435 



perpendicular to the sound beam, and r is the range 

 (see Section 20.4.2). This formula is valid only if 

 both Ai and A2 are greater than the wavelength of 

 the sound, and if either Ai or ^2 is much less than r. 



25.1.7 Target Strength of a Cylinder 



For a cylinder, A2 is infinite in equation (5) and the 

 target strength becomes 



T = 10 log , ^"\ ^ • (6) 



<-7') 



This equation is valid only when the cylinder radius 

 A\ is less than r and the wavelength is less than A\. 



25.2 BEAM ECHOES FROM SUBMERGED 

 SUBMARINES 



At aspect angles within about 20 degrees of the 

 beam, echoes from submarines are produced prima- 

 rily by specular reflection from the pressure hull, the 

 fuel and ballast tanks, and the conning tower (see 

 Section 23.8.1) and are much stronger than echoes 

 at other aspects. Oscillograms show that the echo 

 generally reproduces the outgoing pulse (see Figures 

 25 and 27 in Chapter 23). 



25.2.1 Beam Target Strengths 



Observed submarine target strengths at beam as- 

 pects and at long ranges lie mostly between 20 and 

 30 db. About 25 db is the average value (see Section 

 23.1.1); typical values of 4 1 or 4 2 in equation (4) 

 which would correspond to this target strength would 

 be 500 and 2.5 yd respectively. The observed spread 

 of values may result entirely from experimental 

 errors. 



Off-beam target strengths, foimd at aspects 20 

 degrees or more away from the beam, are reported 

 in Section 25.3. 



Vaeiation with Submarine Class 



Observed diiTerences in the target strengths of 

 different submarines measured both directly and in- 

 directly are less than the estimated experimental 

 error in the direct measurements (see Section 25.2.1). 

 Consequently no reliable overall evaluation of the 

 dependence of the target strength on the class of sub- 

 marine can be made. 



Variation with Submarine Speed 



No significant variation of target strength with 

 submarine speed is expected, since the wake of a sub- 



merged submarine is a poor reflector of sound (see 

 Section 33.3). No pronounced variation has been ob- 

 served in practice for submerged speeds from 1 to 6 

 knots at keel depths of about 100 ft (see Section 23.3). 



Variation with Range 



Theoretically, beam target strengths depend on 

 the range at ranges less than the principal radii of 

 curvature of the submarine at beam aspect (see Sec- 

 tions 20.4.4 and 23.4). For a 517-ton German U- 

 boat, approximated by an ellipsoid with principal 

 radii of curvature of 576 and 2.3 yd, the variation of 

 target with range predicted from equation (5) is 

 shown in Table 1. Although no observations are 



Table 1. Theoretical range variation. 



available to confirm this variation with range', the 

 result is believed to be reliable. 



Variation with Pulse Length 



No marked dependence of target strength on pulse 

 length is expected at beam aspect, since the echo 

 approximately reproduces the pulse (see Section 

 23.5.1). The available evidence is neither very con- 

 sistent nor conclusive, but does not demonstrate any 

 sharp variation in the target strength with the pulse 

 length (see Section 23.5.2). 



Variation with Frequency 



No variation of target strength with frequency is 

 expected theoretically at beam aspects for specular 

 reflection (see Sections 20.4 and 23.6.1). Observa- 

 tions confirm this prediction (see Section 23.6.2), ex- 

 cept for a few measurements at 60 kc; these 60-kc 

 target strengths, however, are so large that calibra- 

 tion errors are believed responsible. 



25.2.2 Echo Structure 



Generally, beam echoes are square-topped and 

 resemble the outgomg pulses (see Section 23.8.1) 

 For very short pulses, beam echoes from submarines 



