To calculate an efficient breathing gas you have to know the maximum operating depth (MOD) at which you are breathing this gas and to decide the equivalent narcotic depth (END) you are willing to experience there.
Components
1. Oxygen
The most important part is the oxygen, cause it is necessary for the metabolism of our cells. An efficient gas should have a partial pressure of oxygen of 1.2 (long dive) til 1.6 (short dive) at the highest depth you want to breath it. If it is higher then that you will possible expirience symptoms of oxygen toxicity. If the MOD is hight enough you can’t breath it at the surface anymore, cause then the percentage of the oxygen is too low (hypoxic).
2. Inert gas
The rest of the gas should be something that isn’t influencing our body and is comparable cheap. The gases that fulfill these demands for technical diving are nitrogen and helium these days.
Nitrogen is cheaper, but earlier narcotic then helium. Empirical tests have shown that it’s possible to expirience symptoms of nitrogen narcosis when breathing air already at 30 meters. Therefore it shouldn’t exceed a partial pressure of 3,16 bar1 for an END (equivalent narcotic depth) value of 30.
1 Ambient pressure (at 30m) * amount of nitrogen (in air) = 4 bar * 0,79 = 3,16 bar
Examples
1. Dive at 25 meter
– Ambient pressure = 3,5 bar
– Amount of oxygen = 1,4 bar / 3,5 bar = 0,40
– Amount of nitrogen = 3,16 bar / 3,5 bar ≈ 0,90
–> EAN 40 (MOD = 25m, END = 25m)
2. Dive at 50 meter
– Ambient pressure = 6 bar
– Amount of oxygen = 1,4 bar / 6 bar ≈ 0,23
– Amount of nitrogen = 3,16 bar / 6 bar ≈ 0,53
– Amount of helium = 1 – 0,23 – 0,53 = 0,24
–> Tx 23/24 (MOD = 50m, END = 30m)