NONSPECULAR REFLECTION 



361 



20.5 REFLECTIONS FROM SUBMARINES 



Expressions were developed in tlie preceding sec- 

 tion for the target strengths of various surfaces in 

 terms of the reflected pressures. These formulas were 

 employed in a theoretical study ' in order to calculate 

 mathematically the target strength of a German 

 submarine. 



From an examination of blueprints of the U570,' a 

 517-ton German U-boat captured by the British 

 early in the war and renamed HMS/M Graph, the 

 radius of curvature of the surface of the hull and 

 corming tower at different points was obtained. In 

 computing the results, the submarine was approxi- 

 mated by an ellipsoid of revolution, whose semi-axes 

 were 110 and 7 ft. The results were then corrected 

 for the reflections from the coiming tower, which was 

 assumed to be a cylinder with a "tear-drop" cross 

 section. 



Target strengths were found from equations (49) 

 through (53) in terms of the range and the radii of 

 curvature for different submarine cross sections; 

 ranges of 8, 12, 16, 200, and 1,000 yd were used. At 

 ranges where the coiming tower did not include a 

 large number of zones, the Fresnel integrals [ob- 

 tained when equation (22) is integrated exactly 

 along the length of a cylinder] were used. The 

 calculations were actually carried out in terms of 

 reflection coefficients, which differ somewhat from 

 target strengths derived in this chapter. The results 

 of these computations are presented in Chapter 23 

 together with the results of the direct and indirect 

 measurements. 



20.6 



NONSPECULAR REFLECTION 



So far only reflections from highlights on a target 

 surface have been discussed. These highlights cor- 

 respond to specular reflections in optics and give 

 much the same predictions as those found from the 

 ray theory. In particular, the echo is assumed to 

 come only from that region of the target where 

 the surface is nearly perpendicular to the incident 

 sound wave. This section discusses those cases 

 where such reflection cannot occur and where the 

 observations cannot be explained in this way. At 

 the present time, however, different types of non- 

 specular reflections have not been identified with 

 any observed reflections from actual targets, so that 

 at most this section can only suggest the theoretical 

 expectations. 



20.6.1 Rough Surfaces 



The most simple type of non.specular reflection is 

 that from a rough surface, that is, a surface whose 

 irregularities are much larger than the wavelength. 

 Practical formulas applying to this kind of nonspecu- 

 lar reflection from various underwater targets are de- 

 rived in reference 6. The wavelength of sound is so 

 much greater than that of light, however, that such 

 reflections, which are common in optics, are not to be 

 expected in underwater acoustics. The presence of 

 bubbles on or near the surface of a target can, how- 

 ever, give rise to a diffuse reflection with sound scat- 

 tered in all directions; the reflection of sound from 

 bubbles is described in detail both theoretically and 

 experimentally in Chapters 26 through 35, which 

 deal with the acoustic properties of wakes. 



20.6.2 



Diffraction 



Another type of nonspecular reflection is that from 

 a surface which has no highlights. Consider, for ex- 

 ample, a smooth rigid plane surface in the form of a 

 square, set at an angle relative to the incident rays. 

 This surface will reflect sound specularly, but not 

 back to the sound source. In addition, however, some 

 sound will be reflected in other directions; some of it 

 will be reflected directly backward. This phenome- 

 non corresponds essentially to the diffracted soimd 

 observed when a wave passes through a square 

 aperture, and the echo intensity will decrease as 

 {yfKY, where y is the length of the square and \ is 

 the wavelength. The Fresnel zone theory may again 

 be appHed, provided that the effects of both the first 

 and last zones are considered. No results have been 

 worked out along this line, however. 



20.6.3 



Scattering 



A third type of nonspecular reflection is that from 

 objects much smaller than the wavelength. The 

 Fresnel zone theory is not applicable to such small 

 targets, and even the basic equation (21) derived in 

 Section 20. 1 is no longer valid, since the derivation 

 assumes that the radius of curvature of the surface is 

 greater than the wavelength. Corresponding analyses 

 have been carried out for targets much smaller than 

 the wavelength; these yield, for a rigid target. 



^ = 20,„g?f, 



(50) 



where V is the volume occupied by the reflecting ob- 



