# 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 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

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

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) [Notes 1] 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