Maximum operating depth

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 a safe limit. This safe limit 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 safe depth for breathing that gas. 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. Note that 21% is the approximate concentration of oxygen in normal air.

Safe limit of partial pressure of oxygen

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

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]

Formulas

To calculate the MOD for a specific pO₂ and percentage of oxygen, the following formulas are used:

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] [2]} is 33 fsw/atm x [(1.4 ata / 0.36) - 1] = 95.3 fsw.

Note that the formula simply divides the absolute partial pressure of oxygen which can be tolerated (expressed in atmospheres) by the fraction of oxygen in the nitrox, 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 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 fsw by multiplying with the appropriate conversion factor, 33 feet of sea water (fsw) per atmosphere. The metric formula is equivalent.

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.

MOD table in feet

Maximum Operating Depth (MOD) in feet of 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.

MOD table in metres

Maximum Operating Depth (MOD) in metres of 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

See also

• Oxygen toxicity

Notes

1. Feet of 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 depth indicated in fsw is gauge pressure (relative to surface pressure) unless specified.

References

1. Lang, M.A. (2001). DAN Nitrox Workshop Proceedings. Durham, NC: Divers Alert Network. p. 52. Retrieved 21 November 2012.
2. "Physics of Diving" (PDF). NOAA Diving Manual. National Oceanic and Atmospheric Administration. Retrieved 6 September 2013.