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Algo 02 NDL Calculation

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matejhron edited this page May 10, 2026 · 2 revisions

Algo-02 — NDL Calculation

The No-Decompression Limit is the maximum bottom time at a given depth such that the diver can ascend directly to the surface without triggering a mandatory deco stop. DecoJS finds it by binary search.

Entry point

// js/decoModel.js:741 (signature)
export function calculateNDL(depth, n2Fraction = N2_FRACTION, gfLow = 1.0)

Returns:

{
  ndl: 20,                    // minutes, floor-rounded for display
  ndlExact: 20.3,             // exact (pre-rounding) value for comparison
  controllingCompartment: 7,  // TC id whose M-value bites first on direct ascent
  descentTime: 2              // minutes to reach depth at DESCENT_SPEED = 20 m/min
}

The NDL returned is bottom time — time at maximum depth after descent completes. Total dive duration is descentTime + ndl.

Why $GF_{low}$, not $GF_{high}$

A common confusion: surely NDL should use $GF_{high}$, since that's the surface limit? Not for "first stop becomes mandatory." The moment a first stop is required, the deco algorithm starts enforcing $GF_{low}$ — so that is the threshold at which the no-deco window closes. Using $GF_{high}$ here would overstate the NDL by pretending the entire GF budget is available immediately.

// js/decoModel.js:802
const { ceilingDepth } = getDiveCeiling(testPressures, gfLow);

Default gfLow = 1.0 (100 %) — raw Bühlmann, no conservatism. Typical planning values like $30/85$ pass gfLow = 0.30, which tightens NDL substantially.

Method — binary search

// js/decoModel.js:754-767 (descent)
const descentTime = depth / DESCENT_SPEED;
const descentRate = (alveolarN2 - getAlveolarN2Pressure(SURFACE_PRESSURE, n2Fraction)) / descentTime;
const afterDescent = {};
COMPARTMENTS.forEach(comp => {
    afterDescent[comp.id] = schreinerEquation(
        initialN2,
        getAlveolarN2Pressure(SURFACE_PRESSURE, n2Fraction),
        descentRate,
        descentTime,
        comp.halfTime
    );
});

Descent is simulated once via Schreiner at DESCENT_SPEED = 20 m/min (js/decoModel.js:720). That gives tissue state at the start of bottom time.

// js/decoModel.js:791-809
while (maxTime - minTime > 0.1) {
    const testTime = (minTime + maxTime) / 2;
    const testPressures = {};
    COMPARTMENTS.forEach(comp => {
        testPressures[comp.id] = haldaneEquation(afterDescent[comp.id], alveolarN2, testTime, comp.halfTime);
    });
    const { ceilingDepth } = getDiveCeiling(testPressures, gfLow);
    if (ceilingDepth > 0) {
        maxTime = testTime; // Needs deco, reduce time
    } else {
        minTime = testTime; // No deco, can go longer
    }
}

For each candidate $t$, apply Haldane at depth for $t$ minutes, then check if the surface ceiling ($GF_{low}$-adjusted) is still zero. Precision 0.1 min (6 s). Upper bound is clamped to 300 min (5 h).

Two early exits bracket the search:

  • If ceiling is already > 0 immediately after descent, return ndl = 0 (very deep dive — descent alone triggers deco).
  • If ceiling at 5 h is still 0, return ndl = Infinity (very shallow — NDL is effectively unbounded).

Worked example

30 m on air, $GF_{low} = 0.30$ (conservative deco-planner setting).

  • Descent: 30 m at 20 m/min = 1.5 min. Schreiner loads all 16 tissues.
  • After descent, TC7 ($T_{1/2} = 54$ min) is leading at roughly 0.85 bar.
  • Binary search converges on ndlExact ≈ 15.6 min; ndl = 15 (floored).
  • Controlling compartment: TC7 (medium-fast; typical for 20–40 m air dives).

For default raw Bühlmann ($gfLow = 1.0$) the same dive yields NDL ≈ 21 min — the conservatism cost of 30/85 is roughly 6 min of bottom time.

Branching in generateDecoProfile

NDL is the pivot in the top-level dive planner:

// js/diveSetup.js:346-367
const { ndl, controllingCompartment } = calculateNDL(maxDepth, bottomGas.n2, gfLowDec);
const descentTime = roundUp(maxDepth / DESCENT_SPEED);
const requiresDeco = bottomTime > ndl;
if (!requiresDeco) {
    const waypoints = generateSimpleProfile(maxDepth, bottomTime, safetyStop, options);
    waypoints[1].gasId = bottomGas.id;
    return {
        waypoints, ndl, requiresDeco: false,
        decoStops: [], totalDecoTime: 0, controllingCompartment
    };
}
// else: proceed to generateDecoSchedule()

If bottomTime ≤ ndl, the planner returns a no-stop profile (optionally with a safety stop). Only when deco is unavoidable does the expensive generateDecoSchedule() pipeline run.

Cross-references

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