# Decompression Model

The mathematical machinery DecoJS uses to track inert gas loading across 16 theoretical tissue compartments and compute ascent limits from them. These pages are the developer-facing counterpart to `pressure.html`, `tissue-loading.html`, `m-values.html`, and `gradient-factors.html` — they assume the reader already knows what inert-gas loading is and want to see the algorithm as it is coded.

For algorithm-level orchestration (how these equations drive a simulated ascent, deco-stop search, NDL computation), see [Algorithms](Algorithms.md). For the JavaScript module/function index, see [Architecture](Architecture.md).

## Notation

Used consistently across all Model pages.

| Symbol | Meaning | Units |
|--------|---------|-------|
| $P_{amb}$ | Ambient (absolute) pressure | bar |
| $P_{alv}$ | Alveolar inert-gas partial pressure | bar |
| $P_t$ | Tissue inert-gas pressure | bar |
| $P_{t,0}$ | Initial tissue inert-gas pressure (segment start) | bar |
| $P_{alv,0}$ | Initial alveolar inert-gas pressure (segment start) | bar |
| $T_{1/2}$ | Compartment half-time | min |
| $k$ | Rate constant, $k = \ln(2) / T_{1/2}$ | min⁻¹ |
| $R$ | Rate of change of alveolar pressure ($dP_{alv}/dt$) | bar/min |
| $a, b$ | Bühlmann M-value coefficients (per compartment, per variant) | $a$: bar; $b$: dimensionless |
| $M$ | M-value, maximum tolerable $P_t$ at a given $P_{amb}$ | bar |
| $GF$ | Gradient factor, fraction of supersaturation budget used | 0–1 internally |

**GF storage convention**: DecoJS UI code (`js/diveSetup.js`) stores GF as percent (`DEFAULT_GF_LOW = 100`, `DEFAULT_GF_HIGH = 100`); algorithmic code in `js/decoModel.js` uses fractions (`DEFAULT_GF_LOW = 1.0`, `DEFAULT_GF_HIGH = 1.0`). Conversion happens at the boundary.

All depths are in meters, all times in minutes.

## Unit constants

Defined at the top of `js/decoModel.js`:

```javascript
// js/decoModel.js:18-30
export const SURFACE_PRESSURE = 1.01325;       // 1 atm exactly, in bar
export const WATER_VAPOR_PRESSURE = 0.0627;    // alveolar H2O correction at 37°C, in bar
export const N2_FRACTION = 0.7902;             // N2 + Ar lumped, per ZH-L convention
export const PRESSURE_PER_METER = 0.1;         // fresh-water convention, bar/m
```

`N2_FRACTION = 0.7902` (not 0.79) is the standard Bühlmann convention — argon (~0.93%) is lumped into the nitrogen compartment because it has similar kinetics. `PRESSURE_PER_METER = 0.1` is the fresh-water value; sea water would be slightly higher but DecoJS uses the rounded educational convention.

## Chapter TOC

1. [Model-01-Compartments](Model-01-Compartments.md) — the 16 ZH-L16 compartments, their half-times, the a/b coefficients, and the A/B/C variants.
2. [Model-02-Haldane-Equation](Model-02-Haldane-Equation.md) — constant-depth tissue loading.
3. [Model-03-Schreiner-Equation](Model-03-Schreiner-Equation.md) — linear-rate-of-pressure-change tissue loading (the workhorse during descent and ascent).
4. [Model-04-M-Values](Model-04-M-Values.md) — Bühlmann M-value lines, ceiling equation, instantaneous GF.
5. [Model-05-Gradient-Factors](Model-05-Gradient-Factors.md) — Baker GFs, `pAnchor`, and the GF ramp.

Cross-cutting: [Algorithms](Algorithms.md) drives these equations across a full dive; [References](References.md) lists primary sources.