The document discusses the factors influencing target strength in sonar applications, including the shape, size, construction, and angle of the targets, as well as the wavelength of the incident sound. It details calculations for target strength in various scenarios such as large spheres, fish with swim bladders, and different geometrical shapes of targets like cylinders and plates. Additionally, it includes examples and equations related to signal levels, scattering, and acoustic characteristics of specific objects.

1. Target Strength
reflected wave
incident wave
a
2
i r
I 4 r I
  
r
i
I
TS 10log
I
 
  
 
scattering cross section
 
2
TS 10log 10log
4 r 4
 
   
 
   
 
   
At r = 1 yd.

2. Factors Determining Target Strength
• the shape of the target
• the size of the target
• the construction of the walls of the target
• the wavelength of the incident sound
• the angle of incidence of the sound

3. Target Strength of a Convex Surface
i 1 2
dP I ds ds

R1
R2
1
d
1
ds
2
d
2
ds
i 1 1 2 2
dP I R d R d
  
Incident Power
Large objects compared to the wavelength

4. Reflected Intensity
1
2 1

1
R
1

1

r
1 1
ds r2d
  
1 2 1 2
dA ds ds r2d r2d
 
   
i 1 1 2 2 i 1 2
r 2
1 2
dP I R d R d I R R
I
dA r2d r2d 4r
 
  
 
R1
R2
1
d
1
ds
2
d
2
ds
r
i
I
TS 10log
I
 
  
 
1 2
R R
TS 10log
4
 
  
 
(At r = 1 m)

5. Special Case – Large Sphere
1 2
R R a
 
2
a a
TS 10log 20log
4 2
   
 
   
 
 
a
Note: 2
a
4 4



2
a
  
Large means
circumference >> wavelength
ka 1

TS positive only if a > 2 yds

6. Large Spheres (continued)
 
2 2 2 2
r
1
2
i
I 1
a a cot J kasin
I 4 r 2
  
 
    
 
 
  
 
a

0o
180o

7. Example
• An old Iraqi mine with a radius of 1.5 m is
floating partially submerged in the Red Sea. Your
minehunting sonar is a piston array and has a
frequency of 15 kHz and a diameter of 5 m. 20
kW of electrical power are supplied to the
transducer which has an efficiency of 40%. If the
mine is 1000 yds in front of you, what is the signal
level of the echo. Assume spherical spreading.

8. Scattering from Small Spheres
(Rayleigh Scattering)
2
2 2
r
4 2
i
I V 3
cos 1
I r 2
  
 
 
  
 
4 2
25
TS 10log ka a
36
 
  
 
ka 1


9. Scattering from Cylinders
L
2a

 
2
2 2
2
aL sin cos
TS 10log
2 1yd
 
   
 
  
  
 
 
 
 
 
2 L
sin

  

 
2
2
aL 1
TS 10log
2 1yd
 
 
  
 

 
 
 
o
0
 
Dimensions (L,a) large
compared to wavelength

10. Gas Bubbles
• Damping effect is due to the
combined effects of radiation,
shear viscosity and thermal
conductivity. A good
approximation is
• where fk is the frequency in kHz.
3
2
2
2
0
0
1
resonant frequency
damping term
bs
a
f
f
f




 
 
 
 
 
 
 
 


 
 
0
3
5
3
1 3.25
1 0.1
2
1000 kg/m
hydrostatic pressure in Pa 10 1 0.1
depth in meters
adiabatic constant for air ( 1.4)
w
w
w
w
P
f z
a a
P z
z

 


  

  

 
0.3
0.03 for 1 kHz< 100 kHz
k k
f f
  

11. Fish
• Main contribution for fish target strength comes from the swim
bladder.
• This gas-filled bladder shows a very strong impedance contrast with
the water and fish tissues. It behaves either as a resonator (frequencies
of 500 Hz-2 kHz depending on fish size and depth) or as a geometric
reflector (> 2 kHz). This swim bladder behaves very similar to gas
bubbles. The difference in target strength between fish with and
without swim bladder can be 10-15 dB.
• A semi-empirical model most often used is:
• Love (1978)
• This formula is valid for dorsal echoes at wavelengths smaller than fish
length L.
19.1log 0.9log 24.9
fish k
TS L f
  

12. 4
2
1a
a
2
r
4
4
2
7
.
61

V
2
ar
r
a
2
4
4
9



2
2
aL
 
2
2 2
sin
aL cos
2
 


2
a
4




2
2
2
cos
sin













 ab
2
2






a
bc
  



 2
2
1
2
cos
2















 J
a
Form
t
TS=10log(t)
Symbols Direction of incidence Conditions
Any convex surface
a1a2 = principal radii of
curvature
r = range
k = 2/wavelength
Normal to surface
ka1, ka2 >>1
r>a
Large Sphere a = radius of sphere Any
ka>>1
r>a
Small Sphere
V = vol. of sphere
 = wavelength
Any
ka<<1
kr>>1
Infinitely long thick
cylinder
a = radius of cylinder
Normal to axis of
cylinder
ka>>1
r > a
Infinitely long thin
cylinder
a = radius of cylinder
Normal to axis of
cylinder
ka<<1
Finite cylinder
L = length of cylinder
a = radius of cylinder
Normal to axis of
cylinder
ka>>1
r > L2/
a = radius of cylinder
 = kLsin
At angle  with normal
Infinite Plane surface Normal to plane
Rectangular Plate
a,b = sides of ractangle
 = ka sin
At angle  to normal in
plane containing side a
r > a2/
kb >> 1
a > b
Ellipsoid
a, b, c = semimajor axis
of ellipsoid
parallel to axis of a
ka, kb, kc >>1
r >> a, b, c
Circular Plate
a = radius of plate
 = 2kasin
At angle  to normal
r > a2/
ka>>1

13. Example
• What is the target strength of a cylindrical
submarine 10 m in diameter and 100 m in
length when pinged on by a 1500 Hz sonar?
2 4 6 8 10
-40
-20
20
40
TS

10o
5o

14. Example
• What is the target strength of a single fish
1m in length if the fish finder sonar has a
frequency of 5000 Hz?