# Limitations of altitude after scuba diving

Recently I went scuba diving in Tenerife. We went for two dives with a maximum depth of 20m on one morning. Duration of the dives was each about 30 minutes. We went with a diving computer that could tell us at which depths we had to stop in order to get the dissolved nitrogen exit our blood stream. This because at greater depth, and thus greater pressure nitrogen dissolves better in your blood. If you rise to quickly it starts to form bubbles, as it no longer stays dissolved in your blood. This can be fatal.

I already knew all of this. However I was surprised to read on my dive computer that I was not allowed to fly for 24 hours. Modern airplanes keep their cabins at a pressure which is equal to the pressure at about 2000m of altitude (which equals about 0.8 bar).

I don't understand why I only had to wait for 5 minutes at a depth of 5m (or 1.5 bar) after diving to a depth of 20m (or 3 bar), but that I had to wait for 24 hours to go from 1 bar to 0.8 bar. The ideal gas law says that P1V1 = P2V2 (assuming equal temperature). So V2 = P1/P2*V1. Thus going from 3 bar to 1.5 bar caused the nitrogen to get twice its original volume, going from 1 bar to 0.8 bar caused the nitrogen to only get 25% larger. Still I only had to wait for 5 minutes in the first case and for 24 hours in the second case! How can this be explained?

• Nitrogen dissolved in your blood is not an ideal gas. The problem is when it starts to form bubbles (which are pretty much an ideal gas). It only takes a small change in pressure to go from dissolved to bubbles (think of a soda can). Commented Jan 31 at 22:05
• Ideal gas law isn't the one you need - Henry's law, which relates the solubility of the gas to the partial pressure is the one to go for. Also remember that on a plane you are in an enclosed tube that ascends very fast - less than 10 min to 10,000 feet and at best will take some minutes, up to several hours to return to ground before you could get medical intervention - better safe than sorry! Good article here
– bob1
Commented Jan 31 at 22:21
• There have been a variety of incidents from scuba diving in mountain lakes, where following the dive tables still resulted in negative outcomes because of the lower pressure at 'lake level'. Commented Jan 31 at 22:49
• @bob1 even Henry's law tells us C = kP, so again it is proportional to the pressure. So it still doesn't make sense. How come that I can halve my pressure in 5 minutes when underwater but that I have to wait 24 hours for a 25% decrease in pressure when I'm above water? Commented Feb 1 at 8:05

I'm no expert, so take this with a grain of salt.

Basically, someone has collected the statistics and done the number crunching and worked out the risk. There is no "one size fits all" scenario here - it could be that you went diving much deeper and for longer or went diving multiple times in one day deep enough to need decompression. So, organizations have put in place guidelines that minimize the chance of an event happening on a plane.

The current recommendations seem to be those on the Divers Alert Network, which show that there are different recommendations depending on what sort of diving and how much diving you have done in the past few days. From this page reproduced below (Copyright: Divers Alert Network, 6 West Colony Place Durham, NC 27705):

Other groups, including some from the armed forces in the USA, have published guidelines for their purposes too. I took this table from here (Source: Scuba.com)

Organization Recommended Surface Interval Before Flying
Divers Alert Network (DAN) 12 hours (minimum)
U.S. Air Force 24 hours
U.S. Navy 2 hours
Professional Association Of Diving Instructors (PADI) 12 hours (for single dives)
18 hours (for multiple dives)
24 hours (ideal recommended interval)

What happens when you dive is that the gasses in your lungs dissolve into the blood stream, but because of the increased partial pressure they also dissolve into tissues, particularly fatty tissues.

Part of the perception problem is that while pressure at depth is linear - for every 10 m (33 feet) you add an additional 1 atmosphere (approx 1 bar, 100,000 kPa) of pressure; but the relative pressure change is curved, not a straight linear relationship. Going from surface 0 m (3.3 f) at 1 atm to 10 m (33 f) at 2 atm is a 200% change, but going from 10 to 20 m (3 atm) is a 150% change. This means that, despite the change in pressure from 1 atm to 0.75 atm being quite small, the relative change compared to even 10 m is quite large. It is this relative pressure that has the biggest effect on barotrauma and decompression sickness. The relative pressure is also what determines how fast the gasses come out of solution. You can read about the physics of hyperbaric pressure and diving at this free book on the NCBI Bookshelf, see the sections on Hydrostatic pressure and Decompression Sickness.

Now, you talk about the "but I only need to wait 5 min at depth". This stop (in addition to the safety stop - checking surface for hazards) is to see that you aren't likely to experience the bends and to dissipate gases that have built up in the blood stream and lungs - a sort of check point to make sure you aren't in trouble and have to descend again. The real decompression is done during your ascent, which should be slow enough to ensure that the dissolved gasses come out; usually 30 feet (9 m) per min. This is a rate that has been worked out to lower (note NOT eliminate) your risk of decompression sickness (DCS). Based on the physics in the book linked above, an ideal ascent would actually get slower as you got closer to the surface. Obviously this is very hard to do in actuality - it would involve some pretty fine control on buoyancy on the divers' part. This slowing may be part of the reason for the 5 m stop, but I can't find any evidence to support this, without going through all the early literature on diving.

I found a relatively recent paper1 that looked at exactly this information giving odds ratios for decompression sickness following flying. The paper looked at 627 dives and gives the odds of DCS relative to flying greater than 28 hours after diving and metres sea water (msw):

Relative to flying > 28 h after diving, the odds of DCS (95% CI) were: 1.02 (0.61, 1.7) 24-28 h; 1.84 (1.0, 3.3) 20-24 h; and 8.5 (3.85, 18.9) < 20 h. Relative to a depth of < 14.7 msw, the odds of DCS (95% CI) were: 1.2 (0.6, 1.7) 14.7-18.5 msw; 2.9 (1.65, 5.3) 18.5-26 msw; and 5.5 (2.96, 1 0.0) > 26 msw.

These numbers mean that if you fly <20 hours after diving you are 8.5x more likely to have DCS than a person who waited 28 hours. And, if you dove deeper than 18.5 msw, you are about 3x more likely to have an event than someone who dove less than 14.5 m

You can still experience decompression sickness up to 7 days post-diving.

In an aeroplane you are again rapidly changing pressure, down to 8,000 feet (2400 m), which equates to about 0.75 bar - big deal you might think. However, you do this ascent over about 15-30 min to reach cruising altitude (source: various flight forums), but I don't know how fast the cabin reaches final pressure. I suspect it does it so that as you reach cruising altitude, the cabin reaches final pressure. This might seem slow, but the risk is real and you are trapped in a tiny, very expensive, metal tube with little hope of medical intervention less than 30 min away. The process looks a little like this:

1. You'd notice the effects (if you have anoxia, you'll feel sleepy and very much not aware of things, so recognition is hard).
2. You notify a flight attendant who a) doesn't have medical training to diagnose properly, only first aid and b) doesn't have the equipment to deal with a medical emergency
3. You get worse - attendant calls for medical professional on plane (may or may not be present) and notifies pilots - they contact Air Traffic Control (ATC), I think they have doctors on call who do an assessment.
4. You get worse - pilots informed, they notify ATC and get diversion to nearest suitable airport.
5. Land, emergency medical team meets you at plane. You still have to transit to somewhere with a hyperbaric chamber - only large city hospitals might have one of these. In 2016 there were only 43 of these capable of treating acute patients in the whole USA2.

This process is very unlikely to take less than 30 min and more likely to take 1-2 hours or (much) longer, depending on where in the world you are. If you are having a gaseous embolism in your heart or brain you need urgent medical attention within an hour or you will have serious life-long complications.

References:

1. Freiberger JJ, Denoble PJ, Pieper CF, Uguccioni DM, Pollock NW, Vann RD. The relative risk of decompression sickness during and after air travel following diving. Aviat Space Environ Med. 2002 Oct;73(10):980-4. PMID: 12398259.

2. Chin W, Jacoby L, Simon O, Talati N, Wegrzyn G, Jacoby R, Proano J, Sprau SE, Markovitz GH, Hsu R, Joo E. Hyperbaric programs in the United States: Locations and capabilities of treating decompression sickness, arterial gas embolisms, and acute carbon monoxide poisoning: survey results. Undersea Hyperb Med. 2016 Jan-Feb;43(1):29-43. PMID: 27000011.

• I am wondering why the navy is being such an outlier here Commented Feb 2 at 18:52
• Hi Bob1, first of all thanks a lot for taking so much time and effort to research my question! Howeverrr I am still confused. You say from 1 bar to 0.75 bar is relatively speaking a big change. It is and it is not. From 1 to 0.75 is a 25% decrease, going from 10m depth to 0m depth is a 100% decrease, or from 20m to 10m a 50% decrease. Both changes are a lot greater then the 1 to 0.75 bar change. And still I only had to do 5 min deco going from 20m to 0m and to fly I had to wait 24 hours. To me it seems out of proportion. Commented Feb 3 at 16:24
• If I would purely look at the physics then I would say that it is safer to dive 10m and hop on the plane immediately after your dive, than diving 20m following the 5min recommended decompression and take no plane at all afterwards. In the one case you go from 2 bar to 0.75 bar, 266% change, in an hour (if you've got priority tickets), in the other case you go from 3 bar to 1 bar, 300% change, in 5 min. Still, in the case of the plane you'd violate recommendations and in the other case not. Commented Feb 3 at 16:29
• @Manziel, this is just a hypothesis, but could the navy be an outlier because they are not so good in keeping their cabins pressurized as commercial planes? An F16 flying at 15km altitude will have its cockpit at a pressure equal to 6km altitude. So it is pressurized but a lot less. At 6km altitude you still have about 0.4 bar. i.sstatic.net/NTyyv.png Commented Feb 3 at 16:37
• Ah scrap that, the navy is an outlier in the sense that they take little time.. Well, I hope they don't go flying an F16 afterwards... Commented Feb 3 at 16:39