There are an amazing number of variables in ocean sound propagation, and a fun trick or two attached to every one of them. Convergence zones and the "deep sound channel" are two interesting examples. There's a brief discussion of these here.

On Sun, Feb 21, 2016 at 9:42 PM, Richard Aiken <xxxxxx@gmail.com> wrote:
On Sun, Feb 21, 2016 at 7:50 PM, <xxxxxx@gmail.com> wrote:
The question hasn't been "How deep can we make the crush depth" for decades. It's
been a combination of  "How deep does this sub need to go?" and "How much are we
willing to pay for a deeper diving sub?".

The only information I have to draw upon (other than "Hunt For Red October" . . .) is that Wikipedia article plus the FAS one. So the following should be taken with this in mind:

In the deep ocean, there are climatic features called "thermoclines," which are layers of sharp temperature differential. Putting a thermocline between yourself and an opposing sonar sensor increases your chances of passing undetected dramatically (all other factors remaining equal). Since - as Tom's response implies - a deeper crush depth will give you more "altitude" to play with, this would in turn put an increased number of potential thermoclines at your disposal.

Because the Alfas were intended to do what
amounted to high speed drive-bys they needed to be able to go extremely deep to avoid
counter attacks (also the deeper you go, the faster you can go before you start getting
cavitation on your props, and cavitation is extremely loud). The Alfas were
special-purpose boats, not standard attack subs, and were very expensive and
maintenance intensive.

From what I read, the Alfas were experimental platforms, intended to test out various advanced technologies. That's why there were only (IIRC) seven of them and why they were relatively quickly mothballed. The Soviets then installed those technologies which had proved useful in subsequent models. (One of these technologies was NOT the Alfa's small oddball nuke plants, which were essentially single-use devices . . . foreign help was needed for the newly-independent Republic of Kazakhstan to avoid an ecological disaster).

-- 
Richard Aiken

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