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.

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. 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.

Formulas

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

In feet

$MOD (fsw) = 33\mathrm{~feet} \times \left [\left ({pO_2\over FO_2} \right ) - 1\right ]$

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

Note that the formula simply divides the total partial pressure of PURE oxygen which can be tolerated (expressed in bar or atmospheres) by the fraction of oxygen in the nitrox, to calculate to total atmospheres pressure this mix can be breathed at (obviously 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 the Earth's air, and the rest is due to depth in water. So the 1 atm for the air is subtracted out, to give the rest of the pressure added by water (in atmospheres). The remaining part in each formula merely converts pressure in atm produced by depth in water, to the depth. It does this by multiplying by the appropriate amount of depth to produce an atmosphere of pressure: 33 feet of sea water (fsw) or 10 meters of sea water.

In metres

$MOD (m) =10\mathrm{~ metres} \times \left [\left ({pO_2\over FO_2} \right ) - 1\right ]$

In which pO₂ is the desired partial pressure in oxygen and the FO₂ is the decimal value of 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 (m) is 10 metres x [(1.4 / 0.36) - 1] = 28.9 metres.

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