Equivalent narcotic depth (END) is used in
technical diving
Technical diving (also referred to as tec diving or tech diving) is scuba diving that exceeds the agency-specified limits of recreational diving for non-professional purposes. Technical diving may expose the diver to hazards beyond those normally ...
as a way of estimating the
narcotic
The term narcotic (, from ancient Greek ναρκῶ ''narkō'', "to make numb") originally referred medically to any psychoactive compound with numbing or paralyzing properties. In the United States, it has since become associated with opiates ...
effect of a
breathing gas
A breathing gas is a mixture of gaseous chemical elements and compounds used for respiration. Air is the most common and only natural breathing gas, but other mixtures of gases, or pure oxygen, are also used in breathing equipment and enclosed h ...
mixture, such as
heliox
Heliox is a breathing gas mixture of helium (He) and oxygen (O2). It is used as a medical treatment for patients with difficulty breathing because mixture generates less resistance than atmospheric air when passing through the airways of the lung ...
and
trimix. The method is, for a given mix and depth, to calculate the depth which would produce the same narcotic effect as when breathing air.
The equivalent narcotic depth of a breathing gas mix at a particular depth is calculated by finding the depth of a dive when breathing air that would have the same total
partial pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas ...
of
nitrogen
Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
and
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
as the breathing gas in question.
For example, a trimix containing 20% oxygen, 40% helium, 40% nitrogen (trimix 20/40) being used at has an END of .
Since air is composed of approximately 21% oxygen and 79% nitrogen, the narcotic gases make up 100% of the mix, or equivalently the fraction of the total gases which are narcotic is 1.0. Oxygen is assumed equivalent in narcotic effect to nitrogen for this purpose. In contrast, the oxygen and nitrogen component in a trimix containing, for example, 40% helium accounts for only 60% of the mix, i.e. a fraction of 0.6. In a trimix, the fraction of narcotic gases (oxygen and nitrogen) is equal to 1.0 minus the fraction of non-narcotic gas (helium).
Calculations
In diving calculations it is assumed unless otherwise stipulated that the atmospheric pressure is 1 bar or 1 atm. and that the diving medium is water.
The ambient pressure at depth is the sum of the hydrostatic pressure due to depth and the atmospheric pressure on the surface.
Metres
The partial pressure of a gas in a mixture at a particular depth in metres is given by:
: fraction of gas × (depth/10 + 1)
So the equivalent narcotic depth can be calculated as follows:
: partial pressure of narcotic gases in air at END = partial pressure of narcotic gases in trimix at a given depth.
or
: (fraction of O
2 + fraction of N
2) in air × (END/10 + 1) = (fraction of O
2 + fraction of N
2) in trimix × (depth/10 +1)
which gives:
: 1.0 × (END/10 + 1) = (fraction of O
2 + fraction of N
2) in trimix × (depth/10 +1)
resulting in:
: END = (depth + 10) × (fraction of O
2 + fraction of N
2) in trimix − 10
Since (fraction of O
2 + fraction of N
2) in a trimix = (1 − fraction of helium), the following formula is equivalent:
END = (depth + 10) × (1 − fraction of helium) − 10
Working the earlier example, for a gas mix containing 40% helium being used at 60 metres, the END is:
:END = (60 + 10) × (1 − 0.4) − 10
:END = 70 × 0.6 − 10
:END = 42 − 10
:END = 32 metres
So at 60 metres on this mix, the diver would feel the same narcotic effect as a dive on air to 32 metres.
Feet
The partial pressure of a gas in a mixture at a particular depth in feet is given by:
: fraction of gas × (depth/33 + 1)
So the equivalent narcotic depth can be calculated as follows:
: partial pressure of narcotic gases in air at END = partial pressure of narcotic gases in trimix at a given depth.
or
: (fraction of O
2 + fraction of N
2) in air × (END/33 + 1) = (fraction of O
2 + fraction of N
2) in trimix × (depth/33 +1)
which gives:
: 1.0 × (END/33 + 1) = (fraction of O
2 + fraction of N
2) in trimix × (depth/33 +1)
resulting in:
: END = (depth + 33) × (fraction of O
2 + fraction of N
2) in trimix − 33
Since (fraction of O
2 + fraction of N
2) in a trimix = (1 − fraction of helium), the following formula is equivalent:
END = (depth + 33) × (1 − fraction of helium) − 33
As an example, for a gas mix containing 40% helium being used at 200 feet, the END is:
:END = (200 + 33) × (1 − 0.4) − 33
:END = 233 × 0.6 − 33
:END = 140 − 33
:END = 107 feet
So at 200 feet on this mix, the diver would feel the same narcotic effect as a dive on air to 107 feet.
Oxygen narcosis
Since there is evidence that oxygen plays a part in the narcotic effects of a gas mixture,
the NOAA diving manual recommends treating oxygen and nitrogen as equally narcotic.
This is now preferred to the previous method of considering only nitrogen as narcotic, since it is more conservative.
In this analysis, it is assumed that the narcotic potentials of nitrogen and oxygen are similar.
Although oxygen has greater lipid solubility than nitrogen and therefore should be more narcotic (
Meyer-Overton correlation), it is likely that some of the oxygen is metabolised, thus reducing its effect to a level similar to that of nitrogen.
References
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Underwater diving safety
Dive planning