Target Strength
 Ir 
TS  10 log  
 Ii 
At r = 1 yd.
  scattering cross section
reflected wave
a
Ii   4r Ir
2
incident wave
  
  
TS  10 log 
 10 log  
2 
 4r 
 4 
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
Target Strength of a Convex Surface
Incident Power
dP  Iids1ds2
dP  Ii R1d1R 2d2
d 2
R2
ds2
ds1
Large objects compared to the wavelength
d1
R1
Reflected Intensity
ds1  r2d1
1
1
dA  ds1ds 2  r2d1r2d2
R1
21
1
r
dP Ii R1d1R 2d2 Ii R 1R 2
Ir 


dA
r2d1r2d2
4r 2
 Ir 
TS  10 log  
 Ii 
R R 
TS  10 log  1 2 
 4 
(At r = 1 m)
R2
d2
ds2
ds1
d1
R1
Special Case – Large Sphere
R1  R 2  a
 a2 
a
TS  10log    20log  
2
 4
Note:
a
 a2

4 4
Large means
circumference >> wavelength
  a 2
ka  1
TS positive only if a > 2 yds
Large Spheres (continued)
Ir
1  2

2
2 2

a  a cot   J1  ka sin   
2 
Ii 4r 
2


180o
a
0o
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.
Scattering from Small Spheres
(Rayleigh Scattering)
I r 2 V 2  3

 4 2  cos   1
Ii  r  2

2
4
 25

TS  10 log   ka  a 2 
 36

ka  1
Scattering from Cylinders
Dimensions (L,a) large
compared to wavelength

2a
L
 aL2   sin  2 cos 2  
TS  10 log 


2
 2     1yd  

2L
sin 

  0o
 aL2  1 
TS  10 log 

2
 2  1yd  
Gas Bubbles
a3
 bs 
2
  f 2 
  0   1   2
 f 



f 0  resonant frequency
  damping term
f0 
1
2 a
3 Pw
w
 w  1000 kg/m3

3.25
1  0.1z
a

Pw  hydrostatic pressure in Pa  105 1  0.1z 
z  depth in meters
  adiabatic constant for air (  1.4)

• Damping effect is due to the
combined effects of radiation,
shear viscosity and thermal
conductivity. A good
approximation is
  0.03 f k0.3 for 1 kHz<f k  100 kHz
• where fk is the frequency in kHz.
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:
TS fish  19.1log L  0.9 log f k  24.9
• Love (1978)
• This formula is valid for dorsal echoes at wavelengths smaller than fish
length L.
t
TS=10log(t)
Form
Symbols
Direction of incidence
Conditions
Any convex surface
a1a2
4
a1a2 = principal radii of
curvature
r = range
k = 2/wavelength
Normal to surface
ka1, ka2 >>1
r>a
Large Sphere
a2
4
a = radius of sphere
Any
ka>>1
r>a
V = vol. of sphere
 = wavelength
Any
ka<<1
kr>>1
a = radius of cylinder
Normal to axis of
cylinder
ka>>1
r>a
a = radius of cylinder
Normal to axis of
cylinder
ka<<1
L = length of cylinder
a = radius of cylinder
Normal to axis of
cylinder
a = radius of cylinder
 = kLsin
At angle  with normal
61.7
Small Sphere
V2

4
ar
2
Infinitely long thick
cylinder
9 4 a 4
Infinitely long thin
cylinder
r

2
aL2
2
Finite cylinder

aL2 sin 
Ellipsoid
 cos 
2
r2
4
Infinite Plane surface
Rectangular Plate

2
2
 ab 
 
 
2
 sin 

 
 bc 
 
 2a 
Normal to plane
2

 cos 2 

2
 a 2  2 J 1   


 cos 2 
    
2
Circular Plate
ka>>1
r > L2/
a,b = sides of ractangle
 = ka sin
At angle  to normal in
plane containing side a
r > a2/
kb >> 1
a>b
a, b, c = semimajor axis
of ellipsoid
parallel to axis of a
ka, kb, kc >>1
r >> a, b, c
a = radius of plate
 = 2kasin
At angle  to normal
r > a2/
ka>>1
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?
TS
40
20
2
4
6
8
10
-20
-40
5o
10o

Example
• What is the target strength of a single fish
1m in length if the fish finder sonar has a
frequency of 5000 Hz?