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Gradient factors explained

Gradient factors are how you add conservatism to a Bühlmann decompression plan. They're written as a pair — GF-low / GF-high, e.g. 30/85 — and they are not a mysterious vendor knob: they are a precise, published idea with a paper trail. Once you understand the two numbers, the whole shape of your ascent makes sense.

Where the limits come from

Staged decompression starts with John Scott Haldane's 1908 work for the Royal Navy: model the body as parallel tissue compartments that take up and release inert gas exponentially, each with its own half-time, and limit how much "extra" gas a tissue may hold during ascent. In 1965 Robert Workman of the US Navy recast those limits as M-values: for each compartment, the maximum inert-gas tension tolerable at a given depth, expressed as a straight line against ambient pressure.

Albert A. Bühlmann, running the hyperbaric laboratory in Zürich, extended this into the ZH-L16 model and — unusually for the field — published the whole thing, coefficients and all, in his book Tauchmedizin. Each of the 16 compartments (nitrogen half-times from 4–5 minutes to 635 minutes, with parallel helium values) carries an a and b coefficient defining its M-value line. That openness is why ZHL-16 variants sit inside most dive computers today, and the "C" set — tuned for real-time computer use — is what DecoLog's planner runs.

The M-value, and why 100% of it is aggressive

An M-value is a ceiling: the most inert-gas tension a compartment may carry at a given ambient pressure before the model considers bubbling likely. Surfacing exactly at the M-value means every millibar of tolerance the model has is spent. The raw limits were derived from real dive trials, but they describe the edge of the envelope, not the middle of it — and decompression sickness is probabilistic, not a switch. Divers wanted a principled way to stay some chosen distance inside the line.

Baker's insight: dive a fraction of the gradient

That principled way came from Erik C. Baker, whose widely circulated papers Understanding M-values and Clearing Up The Confusion About Deep Stops defined the gradient factor: the fraction of the distance between ambient pressure and the M-value that you allow a tissue to occupy. GF 100% is the raw Bühlmann limit; GF 0% is no supersaturation at all. A single worked illustration: suppose a compartment tolerates 1.6 bar of inert tension at the surface (ambient ≈ 1.0 bar). GF-high 85 permits 1.0 + 0.85 × (1.6 − 1.0) = 1.51 bar — you keep 15% of the model's tolerance in your pocket as you surface.

The pair works like this:

Worked example: watch the interpolation

Say a trimix dive produces a first stop at 21 m (≈3.1 ata) with GF 30/85. What fraction applies at the 9 m stop (≈1.9 ata)?

So at 9 m your tissues may occupy 61% of the gap between ambient pressure and their M-values; the stop lasts until the leading compartment decays below that line, then the ceiling moves up. Every stop in a GF schedule is this same computation for whichever compartment is currently in control. Run the same dive at 30/70 and only the shallow stops stretch; run it at 50/85 and the first stop lifts shallower while the total barely moves — this is exactly the experiment worth doing in a planner until the behaviour feels obvious.

The deep-stops correction

For years low GF-low values (10–20) were fashionable, on the intuition — borrowed from bubble models like VPM-B — that stopping deep protects you. Then the US Navy Experimental Diving Unit tested it: the NEDU deep-stops study (David Doolette and colleagues, published 2011) compared a shallow-weighted against a deep-weighted schedule of equal duration and found more decompression sickness on the deep-stops profile — time spent deep keeps your slow tissues on-gassing while you protect fast tissues that didn't need it. Simon Mitchell's lectures on the study brought the result to the technical-diving mainstream. The practical consequence: contemporary guidance has drifted toward moderate GF-low values (commonly 40–60) rather than very deep first stops. Not settled science — but the direction of the evidence is clear enough that "lower GF-low is always safer" should be retired.

Common mistakes

Try it on a real plan

The fastest way to build intuition is to change GF-low and GF-high on a real dive and watch the stops move — first stop depth, shallow-stop time, runtime and gas. DecoLog's planner runs ZHL-16C with any GF pair (and VPM-B beside it, for comparison), free, in your browser.

Try it now — free, in your browser. OPEN THE PLANNER

⚠ Educational only — not a substitute for training or a dive computer. Sources: A. A. Bühlmann, Tauchmedizin; R. D. Workman, US Navy M-value reports; Erik C. Baker, "Understanding M-values" and "Clearing Up The Confusion About Deep Stops"; Doolette et al., NEDU deep-stops study (2011). Choose conservatism with proper instruction and verify every plan.