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Algo 03 First Stop Ramped GF

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matej-hron edited this page Apr 25, 2026 · 4 revisions

Algo-03 — First Stop with Ramped GF

The subtlest chapter. Two coupled questions have to be answered before the deco loop can start:

  1. What is pAnchor? The ambient pressure at which $GF_{max}$ (the controlling tissue's instantaneous gradient factor) first equals $GF_{low}$ during a free ascent.
  2. What is the first stop depth? The shallowest depth to which the diver can ascend, accounting for the fact that the GF ramp already starts at pAnchor — so the GF at destination is not $GF_{low}$ unless the first stop is exactly at pAnchor.

Many naïve implementations conflate the two, or ramp GF from first-stop-depth to surface. DecoJS follows the Baker-intended ramp: from pAnchor to surface. The two converge when first stop = pAnchor; they differ when they do not (e.g., after gas switches).

Subproblem 1: findGFLowAnchor 

// js/decoModel.js:257 (signature)
export function findGFLowAnchor(tissuePressures, currentDepth, n2Fraction, gfLow, ascentRate = ASCENT_SPEED, gasSwitchPoints = null)

Returns {pAnchor, anchorDepth, leadingCompartment, tissuesAtAnchor}.

Method

  1. Simulate an ascent from currentDepth toward surface in 0.1 bar steps (≈ 1 m resolution).
  2. At each step, Schreiner-advance all 16 compartments for the segment and recompute $GF_{max}$.
  3. When $GF_{max}$ first exceeds $GF_{low}$, refine by solving the compartment-ceiling equation for the leading tissue at that exact pressure — rather than accepting the 0.1 bar step boundary.
// js/decoModel.js:286-329
while (currentAmbient > SURFACE_PRESSURE) {
    const nextAmbient = Math.max(SURFACE_PRESSURE, currentAmbient - STEP_SIZE);
    const nextDepth = (nextAmbient - SURFACE_PRESSURE) / PRESSURE_PER_METER;

    // Check for gas switch at this depth (switch to best available gas)
    for (const sp of switches) {
        if (nextDepth <= sp.switchDepth && sp.n2 < currentN2) {
            currentN2 = sp.n2;
            break;
        }
    }

    const depthChange = prevDepth - nextDepth;
    const segmentTime = depthChange / ascentRate;

    if (segmentTime > 0) {
        tissues = simulateDepthChange(tissues, prevDepth, nextDepth, segmentTime, currentN2);
    }

    const { gfMax, leadingCompartment } = calculateMaxGF(tissues, nextAmbient);

    if (gfMax >= gfLow) {
        // Found the step where GF_max crosses GF_low
        // Now calculate the EXACT pAnchor for the leading compartment
        const comp = COMPARTMENTS.find(c => c.id === leadingCompartment);
        const tissuePressure = tissues[leadingCompartment];

        // pAnchor = ceiling at GF_low = (Pt - GF_low * a) / (GF_low/b + 1 - GF_low)
        const exactPAnchor = getCompartmentCeiling(tissuePressure, comp.aN2, comp.bN2, gfLow);
        …
        return { pAnchor: finalPAnchor, anchorDepth: finalAnchorDepth, leadingCompartment, tissuesAtAnchor: { ...tissues } };
    }
    …
}

The final getCompartmentCeiling call is a closed-form solve: given the leading tissue's $P_t$, the exact $P_{amb}$ at which its instantaneous GF equals $GF_{low}$ is its ceiling at that GF. This avoids quantizing pAnchor to 1 m grid boundaries and keeps it numerically precise.

Gas switches during anchor search

If gasSwitchPoints is provided, the 0.1 bar loop consults it at each step and switches $f_{N_2}$ when the simulated ascent crosses a gas's switch depth. Without this, a deco gas with deeper MOD (e.g., EAN50 at 21 m) would be ignored during anchor search, producing a pAnchor as if the diver stayed on bottom gas the whole way up — usually yielding an incorrectly deep pAnchor.

Edge case — dive is within NDL

If the while loop reaches SURFACE_PRESSURE without $GF_{max}$ ever exceeding $GF_{low}$:

// js/decoModel.js:337-345
const { leadingCompartment } = calculateMaxGF(tissues, SURFACE_PRESSURE);
return {
    pAnchor: SURFACE_PRESSURE,
    anchorDepth: 0,
    leadingCompartment,
    tissuesAtAnchor: { ...tissues }
};

pAnchor = 1.01325 bar (surface). The deco loop will then skip all stops — consistent with an NDL dive being queried through this path.

Subproblem 2: findFirstStopWithRampedGF 

// js/decoModel.js:535 (signature)
export function findFirstStopWithRampedGF(tissuePressures, currentDepth, pAnchor, currentN2, gfLow, gfHigh, stopIncrement = 3, gasSwitchPoints = null)

Returns {depth, ambient, tissues} — the shallowest grid-aligned depth at which the tissue ceiling permits staying (using the GF interpolated for that destination), plus the simulated tissue state after the ascent.

Method

Candidate depths are scanned from surface upward, in stopIncrement meters (3 m by default, 0.1 m in continuous mode). For each candidate:

  1. Simulate the ascent from currentDepth to candidateDepth, using _simulateAscentWithGasSwitches when deco gases are provided (applies the correct gas to each depth segment between switches).
  2. Compute the GF at the candidate depth via interpolateGF(candidateAmbient, pAnchor, gfLow, gfHigh).
  3. Compute the dive ceiling under that GF; if ceilingDepth ≤ candidateDepth, the ascent is allowed — return this candidate.
// js/decoModel.js:538-568
for (let candidateDepth = 0; candidateDepth <= currentDepth; candidateDepth += stopIncrement) {
    let simulatedTissues;
    if (gasSwitchPoints && gasSwitchPoints.length > 0) {
        simulatedTissues = _simulateAscentWithGasSwitches(
            tissuePressures, currentDepth, candidateDepth, currentN2, gasSwitchPoints
        );
    } else {
        const ascentTime = (currentDepth - candidateDepth) / ASCENT_SPEED;
        simulatedTissues = ascentTime > 0
            ? simulateDepthChange({ ...tissuePressures }, currentDepth, candidateDepth, ascentTime, currentN2)
            : { ...tissuePressures };
    }

    const candidateAmbient = getAmbientPressure(candidateDepth);
    const gf = interpolateGF(candidateAmbient, pAnchor, gfLow, gfHigh);
    const { ceilingDepth } = getDiveCeiling(simulatedTissues, gf);

    if (ceilingDepth <= candidateDepth) {
        return { depth: candidateDepth, ambient: candidateAmbient, tissues: simulatedTissues };
    }
}

This is the same ascent-permission test used in the deco stop loop itself (see Algo-04-Deco-Stop-Loop) — consistency between first-stop discovery and subsequent stops matters for stop-count agreement across tools.

_simulateAscentWithGasSwitches

// js/decoModel.js:480-507
function _simulateAscentWithGasSwitches(tissuePressures, fromDepth, toDepth, startN2, gasSwitchPoints) {
    let tissues = { ...tissuePressures };
    let currentDepth = fromDepth;
    let currentN2 = startN2;

    const relevantSwitches = gasSwitchPoints
        .filter(sp => sp.switchDepth < currentDepth && sp.switchDepth >= toDepth)
        .sort((a, b) => b.switchDepth - a.switchDepth);

    for (const sp of relevantSwitches) {
        const segmentTime = (currentDepth - sp.switchDepth) / ASCENT_SPEED;
        if (segmentTime > 0) {
            tissues = simulateDepthChange(tissues, currentDepth, sp.switchDepth, segmentTime, currentN2);
        }
        currentDepth = sp.switchDepth;
        currentN2 = sp.n2;
    }

    if (currentDepth > toDepth) {
        const segmentTime = (currentDepth - toDepth) / ASCENT_SPEED;
        tissues = simulateDepthChange(tissues, currentDepth, toDepth, segmentTime, currentN2);
    }

    return tissues;
}

The leading underscore marks this as internal — it is only called by findGFLowAnchor (indirectly) and findFirstStopWithRampedGF. Consumers should not call it directly.

Worked example

40 m on air, 25 min bottom time, $GF = 30/85$.

  • At end of bottom, TC5 ($T_{1/2} = 27$ min) is near-leading with $P_t \approx 2.85$ bar.
  • Anchor search: ascent from 40 m in 0.1 bar steps. Around $P_{amb} \approx 2.4$ bar (≈ 14 m), $GF_{max}$ crosses 0.30.
  • Refinement: for TC5 with $a = 0.6200$, $b = 0.8126$ and $P_t = 2.85$ bar, getCompartmentCeiling(2.85, 0.62, 0.8126, 0.30) resolves pAnchor ≈ 2.40 bar, anchorDepth ≈ 13.9 m.
  • First-stop search (stopIncrement = 3): candidate = 0, 3, 6, 9, 12 all fail ceiling check; candidate = 15 passes. But the GF at 15 m is not $GF_{low}$ — it is interpolateGF(2.5, 2.4, 0.30, 0.85) ≈ 0.36. First stop = 15 m with the post-ascent tissue state, which is slightly off-gassed relative to the bottom state.

In practice, with these inputs first stop ≈ pAnchor rounded up to the 3 m grid; the two values diverge most noticeably when a deco-gas switch during the ascent to first stop changes which compartment leads.

Edge case — pAnchor = SURFACE_PRESSURE

If findGFLowAnchor returned 1.01325 bar (NDL case), the candidate-zero check passes immediately in findFirstStopWithRampedGF — ceiling after a full ascent to 0 m is ≤ 0 m. First stop = 0 m. generateDecoSchedule then takes the no-deco branch (js/decoModel.js:1007).

Cross-references

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