School Targets and Their Acoustic 

 Properties 



The theory applied here with regard to fish 

 schools is very similar to the general approach 

 used for measuring the scattering and absorp- 

 tion of sound in wakes. No dependence is placed 

 on gas bladders within the fish, however, and 

 the target characteristics for the individual 

 fish targets are those obtained by both dynamic 

 and static tests at the NTCF. For lack of 

 additional information regarding the acoustic 

 properties of the fish, the effective absorption 

 cross section, ^ o , is assunned to be about 

 equal to the scattering across section, a « 

 obtained from these tests. 



The assumption is made that the fish school 

 is dispersed so that the distance between 

 neighboring fish is significant. The whole 

 school contains many fish, and some of these 

 fish will not be in the sound beam. Only those 

 fish in the intersection of the sound beam and 

 the school contribute to the acoustic effects. 

 The total number of fish that are effective in 

 producing an echo depends on the width of the 

 school, the angle between the school and 

 the axis of the sound beann, and the 

 area of the sound beam that the school in- 

 tercepts. 



The calculations involving wide schools are 

 different from those which involve narrow 

 schools. In a sonic view of a narrow school, 

 the relative total nunnber of fish in the active 

 reflective volume is small, so that the pro- 

 jected areas of individual fish overlap only 

 rarely. When this condition is fulfilled the 

 school is considered to be narrow. On the other 

 hand, when there are so many fish that their 

 projected areas usually overlap, the school is 

 considered to be wide. 



To obtain a useful approximation for the 

 school target strength the beam pattern of the 

 sonar set nnust be included in the calculation; 

 involved is the area. A, of the sound beam 

 intercepted by the school. The accurate calcu- 

 lation of A is complicated, and the values of 

 many of the quantities entering into it are 

 uncertain. Therefore, a very rough calculation 

 will suffice for the present discussion. If the 

 angular half-width of the sound beam is J3 

 radians in a given plane, then the width of the 

 beam at a range of R yards from the sonar 

 will be 2 R yards. ^ If the school has a verti- 

 cal dimension of Aq yards which is less than 

 the vertical width of the beam at the school, 

 an approximate expression for A is 



2R0Ad 



Note: Because the contractors Involved In this study 

 habitually use the English system of measurement In 

 sonar work this notation will be used throughout. The 

 metric equivalent will be given In parentheses when 

 appropriate. 



The above expression may be substituted into 

 the general target strength expression for the 

 school, which is given as 



N a Aw 

 Ts = 10 log( 4t cos e\ 



where N = average number of fish in a unit 



volume of the school (l/yards ), 

 (T = scattering cross section o£one fish 



(yards^) constant for angled , 

 A= 2 R )? A Q (yards^), 

 w= geometric width of the school 



(yards), 

 d = angle between axis of sound beam 



and perpendicular to the axis of 



the school. 



Introduction of the area expression into the 

 above equation and separation of the expression 

 into two terms give the resulting approxinnate 

 target strength for the narrow school 



Ts= 10 log (^1^:^). 10 log (i^). 



TF 



cos 6 



The first expression contains only the quanti- 

 ties characteristic of the school whereas the 

 second involves quantities describing the posi- 

 tion of the sonar and the bearing and width of 

 the sonar beam. The first term in the expres- 

 sion can be referred to as the strength of the 

 school and nnay be interpreted as the target 

 strength of the school for 1 yard (0,9 m.) of 

 the school. 



In wide schools, the total number of fish in 

 the active volume is so great that overlapping 

 of the projected areas is extensive. If the 

 foregoing equations were used to calculate the 

 power removed from the sound beam, the end 

 result would be that the school removed more 

 power than was incident upon it. This obvious 

 impossibility results from the neglect of the 

 overlapping projected areas in the previous 

 equations. 



The overlapping can be accounted fpr by 

 assxaming that the fish nearest the source casts 

 shadows on those farther away, removing 

 power from the incident sound beam or in the 

 returning echoes, A rough approximation for 

 the foregoing considerations results in an 

 equation for the target strength of the wide 

 school. 



T = 10 log 



Aa 



8t<t, 



1 - e 



-(2N(T w/cos9) 







The foregoing expression is still somewhat 

 rough in that smaller fish would not cast sharp 

 shadows (depending upon the wavelength). 

 Furthermore, second-degree scattering from 

 one fish to another is ignored and only sound 

 scattered once is considered. 



The above equation can be used with the 

 following assumptions: R= 1,600 yards. 



