A pretty interesting video on the NATO Submarine Rescue System (NSRS) is a cooperative project between three NATO countries: France, Norway and the United Kingdom.
“It is designed to rescue personnel from submarines in distress and can dive to depths of up to 600 meters. It consists of three main parts: an intervention system, a rescue vehicle and a transfer under pressure system. It is the largest fly-away submarine rescue system and can dive up to six hours, four times a day. On each dive, it can rescue approximately 12 submariners, who will receive medical treatment in its facilities, if needed. The NATO Submarine Rescue System is available to anyone on request and can be deployed almost anywhere in the world within 72 hours.”
On the downside, while it is ideal for plucking bubbleheads from wrecked Type 209s and the like, running to pick up a 100+ member crew from a U.S. sub would likely push the NSRS to its limit.
The Navy used to have a very robust rescue program of its own, two DSRV’s (Mystic and Avalon) each able to rescue 24 men at a time. Operating from the purpose-built rescue ships USS Pigeon and USS Ortolan, all have since been decommissioned and replaced by the single 16-place Submarine Rescue Diving Recompression System, which is turn is based on the 6-passenger Royal Australian Navy Submarine rescue vehicle Remora and uses craft of opportunity.
