Gas: MOD, END, best mix

What it's for

Breathing-gas basics: oxygen partial pressure, maximum operating depth (MOD), equivalent narcotic depth (END), equivalent air depth (EAD) and the best mix for a depth.

Formulas

$$p{O}_2=F_{O_2}P$$$$MOD=(\frac{p{O}_{2,max}}{F_{O_2}}-P_s)k_w$$$$EN{D}_{O_2}=(P(1-F_{He})-P_s)k_w$$$$EN{D}_{N_2}=EAD=(\frac{P{F}_{N_2}}{0.791}-P_s)k_w$$

Best mix for a depth:

$$F_{O_2}=min(1,\frac{p{O}_2}{P})F_{He}=max(0,1-\frac{P_{END}}{P})$$

• $F_{O_2}$, $F_{He}$, $F_{N_2}$: gas fractions, 0 to 1 (never percent).
• $P$: absolute pressure at the depth, ata. $P_s$: surface pressure, ata. $k_w$: metres per bar.
• $p{O}_2$: oxygen partial pressure, ata. $p{O}_{2,max}$: the limit you choose, ata.
• $P_{END}$: the absolute pressure at the target END depth, ata.
• $0.791$ is the nitrogen fraction of AIR.

The two END models

• 'o2-narcotic' (default): oxygen and nitrogen are narcotic, helium is not. Only the helium share is discounted, so the narcotic pressure is $P(1-F_{He})$.
• 'n2-only': only nitrogen counts, compared against the nitrogen in air. This is the classic equivalent air depth, so ead() is end() with this model.

bestMix and bestFhe size helium using the O₂-narcotic model. The result never exceeds 1 in total, so helium is capped at $1-F_{O_2}$.

Floor at surface and negative values

END can come out negative for a helium-rich mix at shallow depth, meaning it is less narcotic than air at the surface. Pass floorAtSurface: true to clamp the result at the surface (0 m by default).

A negative MOD means the mix is not breathable even at the surface, because $p{O}_{2,max}<F_{O_2}$.

Assumptions and limits

• Fractions are validated: each in 0..1 and fo2 + fhe <= 1. Nitrogen is derived.
• AIR is 20.9% oxygen with the remainder nitrogen (argon lumped in).
• Narcosis is modelled as a simple equivalence, not a physiological prediction.

Sources

• AIR composition: NOAA Diving Manual.

Examples

import { AIR, gas, mod, end, ead, bestMix } from 'dive-math/gas'
mod(gas(0.32), 1.4) // => 33.75
end(gas(0.18, 0.45), 60, { model: 'n2-only' }) // => 22.74
ead(gas(0.32), 30) // => 24.39
end(gas(0.21, 0.35), 5, { floorAtSurface: true }) // => 0
bestMix({ depthM: 30, maxPpo2: 1.4 }).fo2 // => 0.35
mod(AIR, 1.4) // => 56.99

API

See the gas API reference.