Rebreathers

What it's for

Closed-circuit rebreather (CCR) loop maths, semi-closed (SCR) mass balance, and O₂ cell health classification.

Formulas

CCR loop

The loop ppO₂ a CCR can hold is the setpoint, but never above ambient (pure O₂) and never below the diluent's ppO₂:

$$p{O}_{2,loop}=min(P,max(SP,F_{O_2,dil}P))$$

The loop O₂ fraction is $p{O}_{2,loop}/P$. The remaining inert gas is split in the diluent's helium to nitrogen ratio:

$$F_{He}=\frac{(1-F_{O_2})F_{He,dil}}{1-F_{O_2,dil}}$$

• $P$: absolute pressure at depth, ata. $SP$: setpoint, ata.
• $F_{O_2,dil}$, $F_{He,dil}$: diluent fractions. $F_{O_2}$, $F_{He}$: loop fractions.

SCR

Steady-state loop O₂ fraction from an oxygen mass balance:

$$F=\frac{Q{F}_s-{\dot{V}}_{O_2}}{Q-{\dot{V}}_{O_2}}$$

Fresh-gas addition of a passive SCR, where a fixed $1/K$ of each breath is dumped at ambient pressure and replaced:

$$Q=\frac{RMVP}{K}$$

• $Q$: fresh-gas supply, surface L/min. $F_s$: supply O₂ fraction. ${\dot{V}}_{O_2}$: metabolic O₂ uptake, surface L/min.
• $RMV$: respiratory minute volume, L/min. $K$: bellows ratio. $P$: absolute pressure, ata.

O₂ cells

A healthy galvanic cell reads about 4.78 times its air reading in pure oxygen:

$$m{V}_{O_2}\approx 4.78m{V}_{air}$$

Deviation of the measured pure-O₂ reading from that theoretical value sets the verdict:

Deviation	Verdict
above +2.5%	FAIL (high-deviation)
−2.5% to +2.5%	PASS (within-spec)
−5% to −2.5%	QUALIFIED_PENDING (low-deviation)
below −5%	FAIL (ratio-collapse)

Assumptions and limits

• Loop gas is a steady-state idealisation. Real loops lag the setpoint.
• hypoxicFloor uses HYPOXIC_PPO2 = 0.16 ata by default. Some agencies use 0.18. It returns the shallowest depth where the diluent is breathable, or 0 at the surface.
• scrLoopFo2 throws if the supply rate does not exceed the metabolic rate, and is floored at 0.
• Cell classification has ambient limits per brand: Aii 10 to 14 mV and AST 9 to 14 mV. Above the ceiling is a FAIL. Below the manufacturer floor is an ambientFlag: 'low' caution and the verdict still comes from the ratio. Below an absolute floor of 8 mV is a FAIL.
• Greenflash is a solid-state optical sensor, so the ratio test does not apply and classifyO2Cell returns null.

Sources

• SCR mass balance: the standard steady-state SCR mass balance (for example Nuckols et al., US Navy SCR analyses).
• Hypoxic floor: a commonly cited floor in IANTD and TDI trimix standards (some agencies use 0.18).
• O₂ cell classification: implemented from the maintainer's classification rules. The 8 mV floor reflects a known end-of-life dropout signature.

Examples

import { AIR, gas } from 'dive-math/gas'
import { effectivePpo2, loopInertFractions, hypoxicFloor, scrLoopFo2, classifyO2Cell } from 'dive-math/ccr'
effectivePpo2({ setpoint: 1.3, diluent: AIR, depthM: 2 }) // => 1.2
loopInertFractions({ setpoint: 1.3, diluent: gas(0.18, 0.45), depthM: 30 }).fhe // => 0.3704
hypoxicFloor(gas(0.1, 0.7)) // => 6
scrLoopFo2({ supplyFo2: 0.5, supplyRateLpm: 15, vo2Lpm: 1 }) // => 0.4643
classifyO2Cell({ brand: 'Aii', ambientMv: 11, o2Mv: 50 })?.status === 'QUALIFIED_PENDING' // => true

API

See the ccr API reference.