Passive Sonar Equation Range Calculator
Underwater acoustics & naval defense: Model the passive sonar equation, Figure of Merit ($FOM$), Thorpe seawater attenuation, ambient noise floor, and tactical detection range.
Acoustic Source & Environmental Inputs
Sonar Figure of Merit & Detection Range
Figure of Merit (FOM)
--
dB (allowable loss for 50% Pd)
Tactical Detection Range $R_{det}$
--
km (ocean distance)
Ambient Noise Level $NL$
--
dB re 1 µPa (Wenz spectrum)
Seawater Attenuation $\alpha$
--
dB / km (Thorpe formula)
Array Noise Gain ($NL - DI$)
--
dB (beamformed noise floor)
Range in Nautical Miles
--
NM ($1 \text{ NM} = 1.852 \text{ km}$)
Transmission Loss vs Range Curve ($TL$ vs $R$)
Tactical detection boundary occurs precisely where transmission loss ($TL$) intersects the Figure of Merit ($FOM$), satisfying $SE = 0$.
The Passive Sonar Equation Formulation
The signal excess ($SE$) determining target detection probability in an ocean acoustic medium is formulated as:
$$SE = SL - TL - (NL - DI) - DT$$
$$FOM = SL - (NL - DI) - DT = TL(R_{\text{det}})$$
$$\alpha(f) \approx \frac{0.1 f^2}{1 + f^2} + \frac{40 f^2}{4100 + f^2} + 2.75 \times 10^{-4} f^2 + 0.003 \; [\text{dB/km}]$$
Thorpe's empirical formula accounts for chemical relaxation of boric acid ($B(OH)_3$) below 1 kHz and magnesium sulfate ($MgSO_4$) between 1 and 100 kHz.
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