DOMES 



155 



It is important to note that the transmission loss is 

 determined solely by the thickness and density of the 

 dome wall and by the frequency of the transducer and 

 is independent of the transducer directivity, of its 

 position within the dome, and of the dimensions of 

 the latter. 1 ' Thus in particular, with d, />,, and / fixed, 

 the dome may be made of any size and shape, for ex- 

 ample, elongated for streamlining purposes, without 

 the transmission loss being affected. Regarding nu- 

 merical values, equation (1) predicts, for example, 

 that a 50-mi] steel dome at a frequency of 25 kc will 

 have a transmission loss = 1 db. 48 '"' 2 



It will be recalled that the transmission loss is a 

 measure of the total amount of energy removed by 

 the dome from the main beam and diverted into 

 other directions. The fraction of this energy reap- 

 pearing in the direction of specular rellection de- 

 pends on the specular reflection coefficient R. This 

 coefficient gives the ratio of the dome-enclosed trans- 

 ducer response in the direction of specular reflection 

 from the dome surface to that in the direction of the 

 transducer axis. R depends on the transducer fre- 

 quency and on the thickness and density of the dome 

 wall. But R is also determined by the directivity of 

 the transducer, by its position in the dome, and by the 

 dome dimensions. Thus, 



when l<„a'-/4 < A 



R^2Q log f~^ c«.s yl 



(5a) 



when & fl2 /4 > A 



R = 20 log 



P\dk„ 



~9 COS y 



+ 20 log r^i 



+ 20 log 



Br 1 } 



; (5b) 



c The transmission loss is also roughl) independent of the 

 angle of incidence of the enclosed projector beam on the dome 

 wall for angles of incidence less than 50°; for greater angles of 

 incidence the transmission loss increases rapidly, because of pro- 

 pagation with appreciable amplitude of transverse elastic waves 

 in the dome wall. 



'l The acoustic radius a is the radius of the rigid circular 

 piston moving an infinite baffle having a beam width 20 and 

 a directivity index A equal to that of the actual projector 

 [1.42 sin <p = 0.61r//n, A = 20 log (c/2wf<i). see Chapter 4 ]. 



k {) a 2 sec y D 2ira 2 



2/t,i -L\I\J)- 



j k a 2 c 



COS- y Sir a- , iii 



- ss -i /- — jz- lor torpedo-shaped 



domes, 

 = for straight-sided domes; 



F(x) _ 1 



X X 



r, ,*■»"- 



\y 



dv = 1 lor x << 1, 



== ,- for X >> 1, 

 V2 x 



< 1 for all v. 



Here a is the acoustic radius of the transducer;' 1 R , : 

 and R M are the principal radii of curvature in the 

 horizontal and vertical planes of the dome wall at the 

 point of its intersection with the transducer axis; L 

 and I) are the maximum linear and transverse dimen- 

 sions of an approximately ellipsoidal, torpedo-shaped 

 dome or of a straight-sided dome with approximately 

 elliptical cross section; A is the distance from the 

 transducer diaphragm to the dome wall for the train- 

 ing position under consideration; and y is the angle 

 of incidence of the enclosed transducer's beam on the 

 dome wall. 48 - 52 



It is now seen from an examination of equation (4) 

 that the transmission loss of the dome is minimized 

 when the thickness of the dome wall, the density of 

 the dome material, and the frequency of the enclosed 

 projector are as small as possible. These quantities 

 should therefore be chosen accordingly, consistent 

 with the mechanical strength of the dome wall, the 

 seaworthiness of the wall material, and the directiv- 

 ity of the projector. In particular, the dome designer 

 should use light metals such as aluminum and pos- 

 sibly organic materials like rubber; 1 ' shapes of maxi- 



f Thus aluminum, various plastics, and still rubber strength 

 ened mechanically by an expanded metal structure have all 

 been used because of their relatively small density to minimize 

 dome transmission losses and specular reflections. The seaworth- 

 iness of these materials, especially the first two, is open to ques- 

 tion. It is claimed that aluminum easily corrodes in sea water; 

 propel treatment of the metal may, however, render it salt 

 water resistant. ■"> Also, plastics are subject to aging and tem- 

 perature effects. A stiff rubber structure may, however, turn oul 

 to be quite satisfactory.''"' 



