Active Sonar Target Strength Calculator
Naval acoustics & active echo-ranging: Compute monostatic active sonar target strength ($TS$), two-way acoustic transmission loss ($2 TL$), reverberation level, and echo detection range.
Sonar Transmitter & Target Geometry
Echo Return & Active Range Performance
Active Figure of Merit (FOM)
--
dB ($2TL$ allowable limit)
Active Detection Range $R_{max}$
--
km (two-way ping echo)
Two-Way Round Trip Time
--
seconds ($2R / c$)
Acoustic Absorption $\alpha$
--
dB / km (Thorpe attenuation)
Target Strength ($TS$)
--
dB re 1 m² echo cross-section
Range in Nautical Miles
--
NM
Echo Signal-to-Interference vs Range
Active echoes decay quadratically faster than passive signals because sound undergoes two-way spreading and double attenuation ($2TL$).
The Active Sonar Equation Formulation
In active echo ranging, the ping travels to the target, reflects from the hull with Target Strength $TS$, and returns to the transducer:
$$SE = SL - 2TL + TS - (NL - DI) - DT$$
$$2TL(R_{\max}) = SL + TS - (NL - DI) - DT = FOM_{\text{active}}$$
$$TL(R) = 20 \log_{10} R + \alpha R \times 10^{-3}$$
Target strength reflects the equivalent acoustic backscattering cross section: $TS = 10 \log_{10}(\sigma_{bs} / 4\pi)$. For a large submarine at broadside ($90^\circ$ aspect), $TS \approx +25 \text{ dB}$, whereas anechoic elastomer tiles can suppress $TS$ below $+10 \text{ dB}$.
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