Surfacing out of a sunken ship/submarine - Survival Tips
Here is a scary scenario:
Let's say you were in a ship or submarine that sunk to the bottom of the ocean.
No scuba gear, no oxygen tank, nothing.
The depth of the ocean is such that nitrogen levels will affect you significantly if you rapidly rise up to the surface.
Let's say you're 100 feet+ below the surface, no Mariana Trench type deal, but shallow enough to know that you can make it to the top in one breath.
You're able to find an area in the ship that has a pocket of air but know that it won't last long, you take your chances, explore, and find a way out.
You have no other choice but to escape and swim to the surface.
QUESTION
You need to swim as fast as you can to the surface, but know that if you go up too fast, you might pass out or something.
What are your options here for best chance of survival?
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The other answers compare the situation to those where a SCUBA diver has to ascend immediately due to gear malfunction. Since you specifically ask about escaping from a sunken ship/submarine, I wanted to point to references explicitly stating that the same techniques are (or were) used for submarine escape. An article in the Journal of Military and Veterans Health discusses the history of submarine escape:
[Breathing apparatus] escape systems remained prevalent until 1946 when the Royal Navy held an inquiry into escape from sunken submarines. The inquiry found no difference in survival rate between those who used a DSEA [Davis Submarine Escape Apparatus, a breathing apparatus]to escape and those that did so unaided.2 As a result the DSEA was replaced with the ‘free ascent’ or ‘blow and go’ technique. Free ascent involved the crew member beginning the ascent with compressed air in their lungs. During the ascent the submariner breathed out at a controlled rate, allowing air to escape. This was a continual process, as the air expanded in the lungs due the decreasing pressure experienced en route to the surface. To limit the chance of being affected by decompression sickness, the escapee would use the bubbles of expelled air to judge the ascent by staying behind the smaller bubbles. To aid in the escape, a crew member might also use a life jacket or buoyant ring. In this case the rate of ascent was more rapid, which required the submariner to blow more rapidly throughout the journey to the surface. Buoyancy assisted free ascent continues to be practiced by Royal Australian Navy (RAN) submariners at the Submarine Escape and Rescue Centre at HMAS Stirling in Western Australia.
So the advice and techniques talked about for SCUBA emergencies were widely practiced for submarine escape, and are almost certainly the best bet in the absence of the one-person escape suits that became available later.
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Escaping a sunken ship or submarine has some similarities to an emergency ascent in the course of SCUBA diving, but it's not identical to it.
First the differences:
You don't have fins. Without fins, you cannot swim as fast and as efficiently. Fins allow you to limit oxygen consumption by using efficiency-optimized leg muscles. Swimming with arms and feet takes far more energy for less speed. A 100 ft swim is still manageable, but now it depends a lot on your physical (and mental) condition.
You've only been under pressure for a short time. Otherwise, it's almost certain that you would have already drowned. Surface ships can trap pockets of air, but generally they fill up with water quite thoroughly when they sink. Nitrogen loading is determined by time*pressure, not just pressure, and won't generally be a concern.
Submarines are equipped with emergency escape gear. The gear comprises a basic airtight suit with a compressed gas bottle (and a pressure relief valve) to fill it up and produce an extremely rapid buoyant ascent. This allows for ascents from 500+ feet.
Note that submarines also sink differently from surface ships. A ship will equalize to ambient pressure once underwater, as nothing inside it can resist the pressure difference. A submarine will maintain some compartments at near-atmospheric pressure. This delays any nitrogen loading before you actually exit the sub.
Since submarine escape gear supplies one with compressed air, allowing plenty of time for the ascent, DCS is again a concern. In that case, DCS is avoided by ascending as fast as possible - about 80 m/min, 4-8 times faster than when diving - to minimize the amount of time spent of high pressure. The same feat, going fast (in both directions), is what allows freedivers to dive as deep as 100-200 m and come back up without need for spending time in deco.
One thing that's more similar to escaping a sunken submarine than any kind of diving is escaping a sunken submarine. All boat crews and even contractors that go out to sea trials generally receive submarine escape training specific to the boat they're on and the gear it's got, so you'd follow that training.
The similarities include:
Lung overexpansion injuries are possible with even small amounts of compressed air. You need to keep your airway open (exhale). As the water is filling up your vessel, it's equalizing its internal pressure up to the higher ambient pressure. So, if you've taken any breaths on the bottom, you've breathed in compressed air.
Passing out is caused by hypoxia, not by ascent speed. Hyperventilation is useless in a survival situation, as it simply tricks your body into delaying the urge to breathe. That's not needed, as exhaling during the ascent will already do the job of controlling your breathing. Additionally, a dangerously high blood level of CO2 (hypercapnia) takes much longer to reach than a dangerously low blood level of oxygen (hypoxia).
In a scenario less likely IRL (but more likely in a movie), with a large vessel where you have managed to survive on large pockets of air, that air has been compressed to ambient pressure. That turns it into a SCUBA-like scenario where eventual DCS is possible. However, you cannot deco without breathing gas, so there's no choice about it.
In conclusion, your top priority is to reach the surface on your remaining blood oxygen. Hypoxia leads to loss of consciousness, which leads to drowning.
Your second priority, if you're starting the escape on a full breath, is avoiding lung overexpansion injuries by keeping your airway open. Lung overexpansion injuries have a lower fatality rate than drowning.
Avoiding DCS is not a priority at all, because you don't have a compressed air source to buy a meaningful amount of time for deco. Slowing down your ascent so little that you can still do it on one breath will do nothing for you, except increase the risk of failure and drowning. Fortunately, over 90% of DCS cases are survivable.
All in all, you want to get the best ratio of ascent rate to oxygen use rate.
If possible, grab any available buoyant object, because that allows you to ascent with minimal effort.
Absent that, get out and swim up. If you don't get up to speed with buoyancy and light kicks, active swimming will have you use up your blood oxygen at maximum possible rate. In that event, you might as well use your muscles' anaerobic energy stores. Practically, at that stage, you won't be thinking about it anyway.
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Even though the question describes a hypothetical and unlikely situation I think it has some merits as it is somewhat relevant for SCUBA diving also: it describes an emergency uncontrolled SCUBA ascent (swimming or buoyant).
Note that the answer below assumes an absolute emergency only that requires an immediate no-air ascent. As in, you either reach the surface now or you will drown, so all the entailed risks are still a better alternative. Don't try this while SCUBA diving - follow your guide / dive plan!
Also check this guide about managing risks in emergency SCUBA ascents.
Nitrogen levels will only be a problem if there is actually a some amount of nitrogen dissolved in your blood. This will happen over time - and faster the higher the pressure - so your best bet is certainly to not stay in the pressurised zone (i.e. the sunken ship / air pocket / deep water) at the bottom, but escape immediately and ascend at a rate of about 20m/60ft per minute.
If you, for example, end up at 30m depth due to some freak accident and immediately surface again it should theoretically be somewhat ok to resurface without any stops, as you didn't spend a long enough time at depth for significant build-up of nitrogen in the blood. This means that the risk of decompression sickness is not big, but you should not rely on this.
Second important thing: when diving up you'll have to constantly breathe out a (small) amount of air. If you're not doing that the air in your lungs will expand and the resulting pressure will rupture lung cells - this can be deadly! So even if you only have one precious breath of air, breathe out constantly when surfacing. Due to the pressure reducing during the ascent the air in your lungs will actually expand and it will thus not feel like you're "running out of air". (I can't stress the importance of this enough. During SCUBA diving certifications you learn that even an ascent of a couple of meters while holding your breath can damage your lungs seriously.)
Obviously in such an emergency it is also important to make sure that the dive up will go as easy and unhindered: leave everything behind that will hinder you, drop any diving weights, clothes, ... etc.
Once on the surface seek medical attention immediately. You are at high risk of decompression sickness and will likely need treatment in a hyperbaric chamber. Also get out of the water immediately if you can, as you are at risk of becoming unconscious if deco sickness hits you.
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First and foremost: Don't Panic
At 30m, you'll be fine if you can free yourself within about 20 minutes and know what you're doing. That being said, there is a good chance you won't know your exact depth, so the sooner the better is going to be your guiding principle. (At 40m, your time drops to 8 minutes. At 20m, you have 45 minutes.)
PADI and NAUI both publish dive tables and at 30m, they give you 20 minutes and 22 minutes, respectively, before you hit the no-decompression limit.
Note: these are not hard do or die limits and likely include some safety margin. Risk will increase as time increases.
What you'd want to do is a CESA, a Controlled Emergency Swimming Ascent where you try to rise at around 60ft/min (1ft/sec) while constantly exhaling. Note from 30m this should take about 100 seconds. Do not ascend "as rapidly as possible".
Constantly exhaling may seem counter-intuitive but is absolutely necessary to avoid injury. At 30m, the air in your lungs is at 4 atmospheres, which means it'll expand to 4 times the volume if you try and hold your breath and it will rupture your lungs. From first hand experience practicing CESAs, the feeling is strange but it's necessary and you won't run out of air. You will be blowing bubbles the entire way. The normal advice for divers is to say "ahh" the entire way up, because that's how you ensure you didn't accidentally start holding your breath.
Contrary to other answers, do not hyperventilate, as it will only increase your chances of drowning:
As the diver ascends [from 30m] hydrostatic pressure is reduced fourfold with a fourfold reduction in oxygen tensions in alveolar gas, arterial blood, and tissues. The rapidly falling cerebral oxygen pressure may be inadequate for consciousness to be maintained and the diver could drown during ascent.
The danger of hyperventilation applies to all breath hold divers, including snorkel divers and people swimming lengths underwater in pools. The reduction in oxygen pressure when coming to the surface from the bottom of a 2 m deep pool can be enough to cause unconsciousness, and some children have died this way.
You won't feel the need to breathe while ascending, because you will have essentially full lungs the entire trip to the surface. Again, you'll be letting excess air out the whole way to the surface. Yes, it will seem like it is taking a long time and it should.
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