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Decompression Model

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matejhron edited this page May 10, 2026 · 2 revisions

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. For the JavaScript module/function index, see Architecture.

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:

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

Cross-cutting: Algorithms drives these equations across a full dive; References lists primary sources.

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