# Maximum operating depth

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In underwater diving activities such as saturation diving, technical diving and nitrox diving, the maximum operating depth (MOD) of a breathing gas is the depth below which the partial pressure of oxygen (pO2) of the gas mix exceeds an acceptable limit. This limit is based on risk of central nervous system oxygen toxicity, and is somewhat arbitrary, and varies depending on the diver training agency or Code of Practice, the level of underwater exertion planned and the planned duration of the dive, but is normally in the range of 1.2 to 1.6 bar.[1]

The MOD is significant when planning dives using gases such as heliox, nitrox and trimix because the proportion of oxygen in the mix determines a maximum depth for breathing that gas at an acceptable risk. There is a risk of acute oxygen toxicity if the MOD is exceeded.[1] The tables below show MODs for a selection of oxygen mixes. Atmospheric air contains approximately 21% oxygen, and has an MOD calculated by the same method.

## Safe limit of partial pressure of oxygen

Acute, or central nervous system oxygen toxicity is a time variable response to the partial pressure exposure history of the diver and is both complex and not fully understood.

Central nervous system oxygen toxicity manifests as symptoms such as visual changes (especially tunnel vision), ringing in the ears (tinnitus), nausea, twitching (especially of the face), behavioural changes (irritability, anxiety, confusion), and dizziness. This may be followed by a tonic–clonic seizure consisting of two phases: intense muscle contraction occurs for several seconds (tonic phase); followed by rapid spasms of alternate muscle relaxation and contraction producing convulsive jerking (clonic phase). The seizure ends with a period of unconsciousness (the postictal state).[2][3] The onset of seizure depends upon the partial pressure of oxygen in the breathing gas and exposure duration. However, exposure time before onset is unpredictable, as tests have shown a wide variation, both amongst individuals, and in the same individual from day to day.[2][4][5] In addition, many external factors, such as underwater immersion, exposure to cold, and exercise will decrease the time to onset of central nervous system symptoms.[6] Decrease of tolerance is closely linked to retention of carbon dioxide.[7][8][9] Other factors, such as darkness and caffeine, increase tolerance in test animals, but these effects have not been proven in humans.[10][11]

The maximum single exposure limits recommended in the NOAA Diving Manual are 45 minutes at 1.6 bar, 120 minutes at 1.5 bar, 150 minutes at 1.4 bar, 180 minutes at 1.3 bar and 210 minutes at 1.2 bar.[1]

## Formula

The formula simply divides the absolute partial pressure of oxygen which can be tolerated (expressed in atmospheres or bar or bar) by the fraction of oxygen in the breathing gas, to calculate the absolute pressure at which the mix can be breathed. (for example, 50% nitrox can be breathed at twice the pressure of 100% oxygen, so divide by 0.5, etc.). Of this total pressure which can be tolerated by the diver, 1 atmosphere is due to surface pressure of the Earth's air, and the rest is due to the depth in water. So the 1 atmosphere or bar contributed by the air is subtracted to give the pressure due to the depth of water. The pressure produced by depth in water, is converted to pressure in feet sea water (fsw) or metres sea water (msw) by multiplying with the appropriate conversion factor, 33 fsw per atmosphere, or 10 msw per bar.

In feet

${\displaystyle MOD(fsw)=33\mathrm {~fsw/atm} \times \left[\left({pO_{2}\mathrm {~ata} \over FO_{2}}\right)-1\right]}$

In which pO2 is the chosen maximum partial pressure of oxygen in atmospheres absolute and the FO2 is the fraction of oxygen in the mixture. For example, if a gas contains 36% oxygen (FO2 = 0.36) and the limiting maximum pO2 is chosen at 1.4 atmospheres absolute, the MOD in feet of seawater (fsw) [Notes 1] is 33 fsw/atm x [(1.4 ata / 0.36) - 1] = 95.3 fsw.[12]

In metres

${\displaystyle MOD(msw)=10\mathrm {~msw/bar} \times \left[\left({pO_{2}\mathrm {~bar} \over FO_{2}}\right)-1\right]}$

In which pO2 is the chosen maximum partial pressure in oxygen in bar and the FO2 is the fraction of oxygen in the mixture. For example, if a gas contains 36% oxygen and the maximum pO2 is 1.4 bar, the MOD (msw) is 10 msw/bar x [(1.4 bar / 0.36) - 1] = 28.9 msw.

## Tables of MOD

Maximum Operating Depth (MOD) in feet sea water for pO2 1.2 to 1.6
MOD (fsw) % oxygen
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 50 55 60 65 70 75 80 85 90 100
Maximum pO2 (bar) 1.6 1727 847 553 407 319 260 218 187 162 143 127 113 102 92 84 72 63 54 48 42 37 33 29 25 19
1.5 1617 792 517 379 297 242 202 173 150 132 117 104 93 84 77 66 57 49 43 37 33 28 25 22 16
1.4 1507 737 480 352 275 223 187 159 138 121 107 95 85 77 69 59 51 44 38 33 28 24 21 18 13
1.3 1397 682 443 324 253 205 171 145 125 110 97 86 77 69 62 52 45 38 33 28 24 20 17 14 9
1.2 1287 627 407 297 231 187 155 132 113 99 87 77 68 61 55 46 39 33 27 23 19 16 13 11 6

These depths are rounded down to the nearest foot.

Maximum Operating Depth (MOD) in metres sea water for pO2 1.2 to 1.6
MOD (msw) % oxygen
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 50 55 60 65 70 75 80 85 90 100
Maximum pO2 (bar) 1.6 523.3 256.7 167.8 123.3 96.7 78.9 66.2 56.7 49.3 43.3 38.5 34.4 31.0 28.1 25.6 22.0 19.1 16.7 14.6 12.9 11.3 10.0 8.8 7.8 6.0
1.5 490.0 240.0 156.7 115.0 90.0 73.3 61.4 52.5 45.6 40.0 35.5 31.7 28.5 25.7 23.3 20.0 17.3 15.0 13.1 11.4 10.0 8.8 7.6 6.7 5.0
1.4 456.7 223.3 145.6 106.7 83.3 67.8 56.7 48.3 41.9 36.7 32.4 28.9 25.9 23.3 21.1 18.0 15.5 13.3 11.5 10.0 8.7 7.5 6.5 5.6 4.0
1.3 423.3 206.7 134.4 98.3 76.7 62.2 51.9 44.2 38.1 33.3 29.4 26.1 23.3 21.0 18.9 16.0 13.6 11.7 10.0 8.6 7.3 6.3 5.3 4.4 3.0
1.2 390.0 190.0 123.3 90.0 70.0 56.7 47.1 40.0 34.4 30.0 26.4 23.3 20.8 18.6 16.7 14.0 11.8 10.0 8.5 7.1 6.0 5.0 4.1 3.3 2.0

## Notes

1. ^ Feet sea water (fsw) is a unit of pressure. One fsw is equal to the hydrostatic pressure exerted by a standard sea water column of 1 foot height at normal Earth gravity. 33 fsw is approximately equal to one standard atmosphere (atm). A pressure indicated in fsw is gauge pressure (relative to surface pressure) unless specified.

## References

1. ^ a b c Lang, M.A. (2001). DAN Nitrox Workshop Proceedings. Durham, NC: Divers Alert Network. p. 52. Retrieved 21 November 2012.
2. ^ a b Clark & Thom 2003, p. 376.
3. ^ U.S. Navy Diving Manual 2011, p. 44, vol. 1, ch. 3.
4. ^ U.S. Navy Diving Manual 2011, p. 22, vol. 4, ch. 18.
5. ^ Bitterman, N (2004). "CNS oxygen toxicity". Undersea and Hyperbaric Medicine. 31 (1): 63–72. PMID 15233161. Retrieved 29 April 2008.
6. ^
7. ^ Lang 2001, p. 82.
8. ^ Richardson, Drew; Menduno, Michael; Shreeves, Karl, eds. (1996). "Proceedings of rebreather forum 2.0". Diving Science and Technology Workshop: 286. Retrieved 20 September 2008.
9. ^ Richardson, Drew; Shreeves, Karl (1996). "The PADI enriched air diver course and DSAT oxygen exposure limits". South Pacific Underwater Medicine Society Journal. 26 (3). ISSN 0813-1988. OCLC 16986801. Retrieved 2 May 2008.
10. ^ Bitterman, N; Melamed, Y; Perlman, I (1986). "CNS oxygen toxicity in the rat: role of ambient illumination". Undersea Biomedical Research. 13 (1): 19–25. PMID 3705247. Retrieved 20 September 2008.
11. ^ Bitterman, N; Schaal, S (1995). "Caffeine attenuates CNS oxygen toxicity in rats". Brain Research. 696 (1–2): 250–3. doi:10.1016/0006-8993(95)00820-G. PMID 8574677.
12. ^ "Physics of Diving" (PDF). NOAA Diving Manual. National Oceanic and Atmospheric Administration. Retrieved 6 September 2013.

## Sources

• Clark, James M; Thom, Stephen R (2003). "Oxygen under pressure". In Brubakk, Alf O; Neuman, Tom S. Bennett and Elliott's physiology and medicine of diving (5th ed.). United States: Saunders. pp. 358–418. ISBN 978-0-7020-2571-6. OCLC 51607923.
• U.S. Navy Supervisor of Diving (2011). U.S. Navy Diving Manual (PDF). SS521-AG-PRO-010 0910-LP-106-0957, revision 6 with Change A entered. U.S. Naval Sea Systems Command. Retrieved 29 Jan 2015.