The submarine with the larger more sensitive instruments in a quieter environment ought to be able to detect sound levels below that which their active opposition can.
If X amount of noise-energy hits the submarine, it only reflects Y<X of that energy, and only Z<Y of that reflection goes in the right direction to be detected by the opposition. The noise should be louder at the submarine, than at the thing detecting the submarine.
Both of these weigh in favor of the submarine detecting the searcher before the searcher detects the submarine.
No, nothing I was talking about was related to the speed of sound in water (which is where I assume you're getting 0.66 seconds/km, since it's about right). I agree the speed of signal propagation seems unlikely to matter much in most situations.
My point is in this scenario there's no appreciable difference between "if you can hear them, they've already found you" and "if you can hear them, they'll find you in 40 seconds"
The observation that they are "detecting the searcher before the searcher detects the submarine" is academic and inconsequential when we're talking about such a negligible amount of time between detections.
But there is an appreciable difference between "if you can hear them, they've already found you", and "if you can hear them, they might never find you because you can see them looking from farther away than they can see, and they might just be outright searching the wrong area".
All my arguments went to the latter kind of problem, not the former. Your 40 seconds number seems to be based on the speed of signal propagation, not the range at which things can be detected.
Even in the event where they do find you, the arguments I gave would suggest that it would take vastly longer than the speed of signal propogation to do so, because they would have to move closer to you. Giving you substantially more notice than 40 seconds.
I was taking it for granted that knowing the location of an unmanned, expendable sonar buoy or probe before you're discovered is not tactically important.
Now that you have me thinking, it would clearly allow you to stay out of detection range if you had the good fortune for their pings to initiate within your detection range but outside theirs.
I'm fully willing to admit I'm talking out my ass here, but does it not make sense to assume that both a) the active drones are going to be much faster than a submarine trying to maintain silence, and b) there are likely to be many drones converging from different directions if they're searching a known submarine parking spot? Still seems like advantage drones to me
I'm not more of an expert of submarine tactics than you are, I was just taking issue with the physical claim that they already know where you are by the time you hear them.
The path loss for active sonar is, logarithmically, twice the path loss for passive sonar. If the signal is 0 dB at 1 meter, it will be -40 dB at 10 km away (barring SOFAR, a regions these submarines probably try to avoid, and ignoring the reflections off the surface and seafloor), and the reflection (assuming an isotropic reflector) will be -80 dB. At 100 km, it's -50 dB and -100 dB.
So, if both sides can detect a -50 dB signal, the passive-sonar target will be able to detect the active-sonar probe 100 km away, while the active-sonar target will be able to detect the reflection from the passive-sonar reflector 0.316 km away. Or maybe 0.315. And that's assuming perfect discrimination.
(By transmitting a signal you can barely detect, you can reduce this discrepancy: if you reduce the signal amplitude by 30 dB at 1 m in this example, the probe can detect the target at 10 m, or maybe 11 m, but the target can't detect it until they're within 100 m.)
However, this massive advantage for passive sonar only really true if it's just as easy for the target to recognize the signal as it is for the probe. In fact, the probe has a huge advantage: it knows what the signal was. If it's just an ordinary chirp, this is of no help, because that's easy to recognize, unless you confuse it for a humpback whale song or something. But if it's Gaussian white noise, it's impossible for a single hydrophone to distinguish from the background noise of the ocean, except by amplitude. Advantage: probe.
But that's a single hydrophone. In fact, though, a point source of white noise is the easiest thing for a phased-array beamforming passive-sonar system to localize. The Triomphant is 138 m long, so if you stuck hydrophones all along its length, you could detect directional sources of sound with an angular precision of about λ/d, the one-dimensional Airy limit. The λ for your active sonar needs to be chosen to be small with respect to the targets you're looking at so it doesn't just diffract around them, so this is probably on the order of 0.1 radians, about 5 degrees.
Two can play that game, though, or thousands. The network of tiny drones can form a single ocean-sized phased array by squirting data back and forth over short-range ultrasound or laser links.
But guess who already has ocean-sized phased arrays of hydrophones for passive sonar?
