Target Strength

reflected wave

incident wave

a

2i rI 4 r I

r

i

ITS 10log

I

scattering cross section

2TS 10log 10log

4 r 4

At r = 1 yd.

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

i 1 2dP I ds ds

R1

R2

1d1ds

2d

2ds

i 1 1 2 2dP I R d R d

Incident Power

Large objects compared to the wavelength

Reflected Intensity

12 11R

11

r

1 1ds r2d

1 2 1 2dA ds ds r2d r2d

i 1 1 2 2 i 1 2r 2

1 2

dP I R d R d I R RI

dA r2d r2d 4r

R1

R2

1d1ds

2d

2ds

r

i

ITS 10log

I

1 2R RTS 10log

4

(At r = 1 m)

Special Case – Large Sphere

1 2R R a

2a aTS 10log 20log

4 2

a

Note: 2a

4 4

2a

Large means circumference >> wavelength

ka 1

TS positive only if a > 2 yds

Large Spheres (continued)

2 2 2 2r12

i

I 1a a cot J ka sin

I 4 r 2

a

0o180o

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)

22 2r

4 2i

I V 3cos 1

I r 2

4 225TS 10log ka a

36

ka 1

Scattering from Cylinders

L

2a

22 2

2

aL sin cosTS 10log

2 1yd

2 Lsin

2

2

aL 1TS 10log

2 1yd

o0

Dimensions (L,a) large compared to wavelength

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

22

20

0

1

resonant frequency

damping term

bs

a

f

f

f

0

3

5

31 3.251 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

Pf z

a a

P z

z

0.30.03 for 1 kHz< 100 kHzk kf f

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 0.9 log 24.9fish kTS L f

421aa

2r

4

4

2

7.61V

2

ar

ra

2

449

2

2aL

22 2sinaL cos

2

2a

4

2

22

cossin

ab

2

2

a

bc

2

2

12

cos2

Ja

Formt

TS=10log(t)Symbols Direction of incidence Conditions

Any convex surface

a1a2 = principal radii of

curvaturer = rangek = 2/wavelength

Normal to surfaceka1, ka2 >>1

r>a

Large Sphere a = radius of sphere Anyka>>1r>a

Small SphereV = vol. of sphere = wavelength

Anyka<<1kr>>1

Infinitely long thick cylinder

a = radius of cylinderNormal to axis of cylinder

ka>>1r > a

Infinitely long thin cylinder

a = radius of cylinderNormal to axis of cylinder

ka<<1

Finite cylinder

L = length of cylindera = 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 Platea,b = sides of ractangle = ka sin

At angle to normal in plane containing side a

r > a2/kb >> 1a > b

Ellipsoida, b, c = semimajor axis of ellipsoid

parallel to axis of aka, kb, kc >>1r >> a, b, c

Circular Platea = 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?

2 4 6 8 10

-40

-20

20

40TS

10o5o

Example

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